A significance test for the lasso
Open accessAbstract
In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic based on lasso fitted values, called the covariance test statistic, and show that when the true model is linear, this statistic has an $\operatorname{Exp}(1)$ asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in the current lasso model). Our proof of this result for the special case of the first predictor to enter the model (i.e., testing for a single significant predictor variable against the global null) requires only weak assumptions on the predictor matrix $X$. On the other hand, our proof for a general step in the lasso path places further technical assumptions on $X$ and the generative model, but still allows for the important high-dimensional case $p>n$, and does not necessarily require that the current lasso model achieves perfect recovery of the truly active variables. Of course, for testing the significance of an additional variable between two nested linear models, one typically uses the chi-squared test, comparing the drop in residual sum of squares (RSS) to a $\chi^{2}_{1}$ distribution. But when this additional variable is not fixed, and has been chosen adaptively or greedily, this test is no longer appropriate: adaptivity makes the drop in RSS stochastically much larger than $\chi^{2}_{1}$ under the null hypothesis. Our analysis explicitly accounts for adaptivity, as it must, since the lasso builds an adaptive sequence of linear models as the tuning parameter $\lambda$ decreases. In this analysis, shrinkage plays a key role: though additional variables are chosen adaptively, the coefficients of lasso active variables are shrunken due to the $\ell_{1}$ penalty. Therefore, the test statistic (which is based on lasso fitted values) is in a sense balanced by these two opposing properties—adaptivity and shrinkage—and its null distribution is tractable and asymptotically $\operatorname{Exp}(1)$.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Unlike stepwise variable selection procedures, LARS does not over-inflate effect size estimates during variable selection nor bias hypothesis tests of those effect sizes.
“Unlike stepwise variable selection procedures, LARS does not over-inflate effect size estimates during variable selection,14 nor bias hypothesis tests of those effect sizes.19”
From A structured approach to hypotheses involving continuous exposures over the life course (2016) · cites this paper as [19]
Stepwise regression would introduce biases that LARS is known to overcome.
“However, stepwise regression would introduce biases that LARS is known to overcome,19 and we have previously discussed how the grouped lasso and elastic net methods would result in the identification of needlessly complicated hypotheses.13”
From A structured approach to hypotheses involving continuous exposures over the life course (2016) · cites this paper as [19]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482 · see citing works
Self-citationThe Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970 · see citing works
Self-citationThe Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162 · see citing works
Self-citationDonoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994 · see citing works
Regularization and Variable Selection Via the Elastic Net
Zou, H., & Hastie, T. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00503.x · Cited by 20,957 · see citing works
Regularization Paths for Generalized Linear Models via Coordinate Descent
Friedman, J., Hastie, T., & Tibshirani, R. (2010) · Journal of Statistical Software · doi:10.18637/jss.v033.i01 · Cited by 19,927 · see citing works
Self-citationDonoho, D. L. (2004) · Cited by 17,049 · see citing works
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
Lu, Z. Q. J. (2010) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2010.00646_6.x · Cited by 12,904 · see citing works
Boyd, S. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984616 · Cited by 12,863 · see citing works
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952 · see citing works
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357 · see citing works
Self-citationNear-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Candès, E. J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.885507 · Cited by 6,973 · see citing works
Atomic Decomposition by Basis Pursuit
Chen, S. S., Donoho, D. L., & Saunders, M. A. (1998) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827596304010 · Cited by 6,734 · see citing works
Estimation of the Mean of a Multivariate Normal Distribution
Stein, C. M. (1981) · The Annals of Statistics · doi:10.1214/aos/1176345632 · Cited by 2,795 · see citing works
Meinshausen, N., & Bühlmann, P. (2010) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2010.00740.x · Cited by 2,314 · see citing works
On Model Selection Consistency of Lasso
Zhao, P., & Yu, B. (2006) · Cited by 2,266 · see citing works
Pathwise coordinate optimization
Friedman, J. H., Hastie, T. J., Höfling, H., & Tibshirani, R. J. (2007) · The Annals of Applied Statistics · doi:10.1214/07-aoas131 · Cited by 1,906 · see citing works
Self-citationExtreme value theory : an introduction
de Haan, L., & Ferreira, A. M. (2006) · EUR Research Repository (Erasmus University Rotterdam) · Cited by 1,310 · see citing works
Wainwright, M. J. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2016018 · Cited by 1,202 · see citing works
On Model Selection Consistency of Lasso
ZhaoPeng, & Yubin, Y. (2006) · Journal of Machine Learning Research · doi:10.5555/1248547.1248637 · Cited by 1,022 · see citing works
On asymptotically optimal confidence regions and tests for high-dimensional models
van de Geer, S., Bühlmann, P., Ritov, Y., & Dezeure, R. (2014) · The Annals of Statistics · doi:10.1214/14-aos1221 · Cited by 1,016 · see citing works
Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models
Zhang, C., & Zhang, S. S. (2013) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12026 · Cited by 1,011 · see citing works
On the “degrees of freedom” of the lasso
Zou, H., Hastie, T. J., & Tibshirani, R. J. (2007) · The Annals of Statistics · doi:10.1214/009053607000000127 · Cited by 962 · see citing works
Self-citationHuman Immunodeficiency Virus Reverse Transcriptase and Protease Sequence Database
Shafer, R. W., Stevenson, D., & Chan, B. K. (1999) · Nucleic Acids Research · doi:10.1093/nar/27.1.348 · Cited by 907 · see citing works
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
Becker, S., Bobin, J., & Candès, E. J. (2009) · Cited by 897 · see citing works
A new approach to variable selection in least squares problems
Osborne, M. R. (2000) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/20.3.389 · Cited by 861 · see citing works
L 1-Regularization Path Algorithm for Generalized Linear Models
Park, M. Y., & Hastie, T. J. (2007) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2007.00607.x · Cited by 859 · see citing works
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
Becker, S., Bobin, J., & Candès, E. J. (2011) · SIAM Journal on Imaging Sciences · doi:10.1137/090756855 · Cited by 848 · see citing works
Human immunodeficiency virus reverse transcriptase and protease sequence database
Rhee, S. (2003) · Nucleic Acids Research · doi:10.1093/nar/gkg100 · Cited by 818 · see citing works
Osborne, M. R., Presnell, B., & Turlach, B. A. (2000) · Journal of Computational and Graphical Statistics · doi:10.2307/1390657 · Cited by 705 · see citing works
Confidence Intervals and Hypothesis Testing for High-Dimensional RegressionPreprint
Javanmard, A., & Andrea Montanari, A. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.3171 · Cited by 654 · see citing works
Templates for convex cone problems with applications to sparse signal recovery
Becker, S., Candès, E. J., & Grant, M. C. (2011) · Mathematical Programming Computation · doi:10.1007/s12532-011-0029-5 · Cited by 608 · see citing works
How Biased is the Apparent Error Rate of a Prediction Rule?
Efron, B. (1986) · Journal of the American Statistical Association · doi:10.2307/2289236 · Cited by 587 · see citing works
High-dimensional variable selectionPreprint
Wasserman, L., & Roeder, K. (2009) · Cited by 540 · see citing works
Extreme Value Theory: An Introduction
Michailidis, G. C., & Stoev, S. (2007) · Technometrics · doi:10.1198/tech.2007.s684 · Cited by 517 · see citing works
The lasso problem and uniqueness
Tibshirani, R. J. (2013) · Electronic Journal of Statistics · doi:10.1214/13-ejs815 · Cited by 514 · see citing works
Self-citationNear-ideal model selection by ℓ1 minimization
Candès, E. J., & Plan, Y. (2008) · Cited by 469 · see citing works
Estimation of Parameters and Large Quantiles Based on the k Largest Observations
Weissman, I. (1978) · Journal of the American Statistical Association · doi:10.1080/01621459.1978.10480104 · Cited by 468 · see citing works
Scaled sparse linear regression
Sun, T., & Zhang, C.-H. (2012) · Biometrika · doi:10.1093/biomet/ass043 · Cited by 463 · see citing works
p -Values for High-Dimensional Regression
Meinshausen, N., Meier, L., & Bühlmann, P. (2009) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.tm08647 · Cited by 447 · see citing works
High-dimensional variable selection
Wasserman, L., & Roeder, K. (2009) · The Annals of Statistics · doi:10.1214/08-aos646 · Cited by 375 · see citing works
Persistence in high-dimensional linear predictor selection and the virtue of overparametrization
Greenshtein, E., & Ritov, Y. (2004) · Bernoulli · doi:10.3150/bj/1106314846 · Cited by 362 · see citing works
Degrees of freedom in lasso problems
Tibshirani, R. J., & Taylor, J. (2012) · doi:10.1184/r1/6586544.v1 · Cited by 333 · see citing works
Self-citationRecovery of Exact Sparse Representations in the Presence of Bounded Noise
Fuchs, J.-J. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.855614 · Cited by 321 · see citing works
Near-ideal model selection by ℓ1 minimization
Candès, E. J., & Plan, Y. (2009) · The Annals of Statistics · doi:10.1214/08-aos653 · Cited by 303 · see citing works
Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression
Fan, J., Guo, S., & Hao, N. (2011) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2011.01005.x · Cited by 264 · see citing works
Degrees of freedom in lasso problems
Tibshirani, R. J., & Taylor, J. (2012) · The Annals of Statistics · doi:10.1214/12-aos1003 · Cited by 239 · see citing works
Self-citationStatistical significance in high-dimensional linear models
Bühlmann, P. (2013) · Bernoulli · doi:10.3150/12-bejsp11 · Cited by 196 · see citing works
Javanmard, A., & Andrea Montanari, A. (2014) · IEEE Transactions on Information Theory · doi:10.1109/tit.2014.2343629 · Cited by 137 · see citing works
Estimation of parameters and large quantiles based on the K largest observations
Weissman, I. (1978) · Advances in Applied Probability · doi:10.1017/s0001867800030561 · Cited by 134 · see citing works
Validity of the expected Euler characteristic heuristic
Taylor, J., Takemura, A., & Adler, R. J. (2005) · The Annals of Probability · doi:10.1214/009117905000000099 · Cited by 104 · see citing works
Self-citationA Perturbation Method for Inference on Regularized Regression Estimates
Minnier, J., Tian, L., & Cai, T. (2011) · Journal of the American Statistical Association · doi:10.1198/jasa.2011.tm10382 · Cited by 102 · see citing works
Statistical Inference After Model Selection
Berk, R. A., Brown, L., & Zhao, L. H. (2009) · Journal of Quantitative Criminology · doi:10.1007/s10940-009-9077-7 · Cited by 90 · see citing works
Adaptive Confidence Intervals for the Test Error in Classification
Laber, E. B., & Murphy, S. A. (2011) · Journal of the American Statistical Association · doi:10.1198/jasa.2010.tm10053 · Cited by 61 · see citing works
L1 Regularization Path Algorithm for Generalized Linear Models
Jing, Y. (2008) · Journal of Jiamusi University · Cited by 60 · see citing works
P-values for high-dimensional regressionPreprint
Meinshausen, N., Meier, L., & Bühlmann, P. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0811.2177 · Cited by 37 · see citing works
Nearly optimal sample size in hypothesis testing for high-dimensional regression
Javanmard, A., & Andrea Montanari, A. (2013) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2013.6736695 · Cited by 32 · see citing works
Confidence Intervals for Low-Dimensional Parameters With High-Dimensional DataPreprint
Zhang, C., & Zhang, S. S. (2011) · arXiv (Cornell University) · Cited by 29 · see citing works
Sequential Selection Procedures and False Discovery Rate ControlPreprint
G’Sell, M., Wager, S., Chouldechova, A., & Tibshirani, R. J. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1309.5352 · Cited by 16 · see citing works
Self-citationAdaptive testing for the graphical lassoPreprint
G’Sell, M., Taylor, J., & Tibshirani, R. J. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1307.4765 · Cited by 15 · see citing works
Self-citationTests in adaptive regression via the Kac-Rice formulaPreprint
Taylor, J., Loftus, J. R., & Tibshirani, R. J. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1308.3020 · Cited by 15 · see citing works
Self-citationEstimation of parameters and large quantiles based on the K largest observations
Weissman, I. (1978) · Advances in Applied Probability · doi:10.2307/1426930 · Cited by 9 · see citing works
van de Geer, S. (2013) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2013.03.006 · Cited by 6 · see citing works
False Discovery Rate Control for Sequential Selection Procedures, with Application to the LassoPreprint
G’Sell, M., Wager, S., Chouldechova, A., & Tibshirani, R. J. (2013) · arXiv (Cornell University) · Cited by 6 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Statistical predictions with glmnet
Engebretsen, S., & Bohlin, J. (2019) · Clinical Epigenetics · doi:10.1186/s13148-019-0730-1 · Cited by 1,212 · see citing works
Tau and Aβ imaging, CSF measures, and cognition in Alzheimer’s disease
Brier, M. R., Gordon, B., Friedrichsen, K., McCarthy, J., Stern, A., Christensen, J., Owen, C., Aldea, P., Su, Y., Hassenstab, J., et al. (2016) · Science Translational Medicine · doi:10.1126/scitranslmed.aaf2362 · Cited by 734 · see citing works
Exact post-selection inference, with application to the lasso
Lee, J. D., Sun, D. L., Sun, Y., & Taylor, J. (2016) · The Annals of Statistics · doi:10.1214/15-aos1371 · Cited by 733 · see citing works
Self-citationControlling the false discovery rate via knockoffs
Barber, R. F., & Candès, E. J. (2015) · The Annals of Statistics · doi:10.1214/15-aos1337 · Cited by 698 · see citing works
Detecting and quantifying causal associations in large nonlinear time series datasets
Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., & Sejdinović, D. (2019) · Publication Database PIK (Potsdam Institute for Climate Impact Research (PIK)) · Cited by 713 · see citing works
Confidence Intervals and Hypothesis Testing for High-Dimensional RegressionPreprint
Javanmard, A., & Andrea Montanari, A. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.3171 · Cited by 654 · see citing works
Panning for Gold: ‘Model-X’ Knockoffs for High Dimensional Controlled Variable Selection
Candès, E. J., Fan, Y., Janson, L., & Lv, J. (2018) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12265 · Cited by 635 · see citing works
Machine learning advances for time series forecasting
Masini, R., Medeiros, M. C., & Mendes, E. F. (2021) · Journal of Economic Surveys · doi:10.1111/joes.12429 · Cited by 544 · see citing works
A practical guide to selecting models for exploration, inference, and prediction in ecology
Tredennick, A. T., Hooker, G., Ellner, S. P., & Adler, P. B. (2021) · Ecology · doi:10.1002/ecy.3336 · Cited by 475 · see citing works
McNeish, D. (2015) · Multivariate Behavioral Research · doi:10.1080/00273171.2015.1036965 · Cited by 437 · see citing works
Statistical learning and selective inference
Taylor, J., & Tibshirani, R. J. (2015) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1507583112 · Cited by 398 · see citing works
Self-citationExact Post-Selection Inference for Sequential Regression Procedures
Tibshirani, R. J., Taylor, J., Lockhart, R., & Tibshirani, R. J. (2016) · Journal of the American Statistical Association · doi:10.1080/01621459.2015.1108848 · Cited by 346 · see citing works
Self-citationDunn, E. C., Soare, T. W., Zhu, Y., Simpkin, A. J., Suderman, M. J., Klengel, T., Smith, A. D. A. C., Ressler, K. J., & Relton, C. L. (2019) · Biological Psychiatry · doi:10.1016/j.biopsych.2018.12.023 · Cited by 315 · see citing works
Tutorial in biostatistics: data‐driven subgroup identification and analysis in clinical trials
Lipkovich, I., Dmitrienko, A., & B., R. (2017) · Statistics in Medicine · doi:10.1002/sim.7064 · Cited by 291 · see citing works
A general theory of hypothesis tests and confidence regions for sparse high dimensional models
Ning, Y., & Liu, H. (2017) · The Annals of Statistics · doi:10.1214/16-aos1448 · Cited by 283 · see citing works
SLOPE—Adaptive variable selection via convex optimization
Bogdan, M., van den Berg, E., Sabatti, C., Su, W., & Candès, E. J. (2015) · The Annals of Applied Statistics · doi:10.1214/15-aoas842 · Cited by 260 · see citing works
Computer age statistical inference algorithms, evidence, and data science
Efron, B., & Hastie, T. J. (2016) · Thammasat University Digital Collections · Cited by 254 · see citing works
High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi
Dezeure, R., Bühlmann, P., Meier, L., & Meinshausen, N. (2015) · Statistical Science · doi:10.1214/15-sts527 · Cited by 231 · see citing works
Optimal Inference After Model SelectionPreprint
Fithian, W., Sun, D. L., & Taylor, J. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1410.2597 · Cited by 269 · see citing works
Self-citationMultivariable Modeling Strategies
Harrell, F. E. (2015) · Springer Series in Statistics · doi:10.1007/978-3-319-19425-7_4 · Cited by 221 · see citing works
Lassopack: model selection and prediction with regularized regression in Stata
Ahrens, A., Hansen, C. B., & Schaffer, M. E. (2020) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x20909697 · Cited by 212 · see citing works
Lenters, V. C., Portengen, L., Rignell‐Hydbom, A., Jönsson, B., Lindh, C. H., Piersma, A. H., Toft, G. V., Bonde, J. P., Heederik, D. J. J., Rylander, L., et al. (2015) · Environmental Health Perspectives · doi:10.1289/ehp.1408933 · Cited by 216 · see citing works
Back to the basics: Rethinking partial correlation network methodology
Williams, D. R., & Rast, P. (2019) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12173 · Cited by 208 · see citing works
Debiasing the lasso: Optimal sample size for Gaussian designs
Javanmard, A., & Andrea Montanari, A. (2018) · The Annals of Statistics · doi:10.1214/17-aos1630 · Cited by 189 · see citing works
Lazarevic, N., Barnett, A. G., Sly, P. D., & Knibbs, L. D. (2019) · Environmental Health Perspectives · doi:10.1289/ehp2207 · Cited by 184 · see citing works
Dunn, E. C., Soare, T. W., Raffeld, M. R., Busso, D. S., Crawford, K. M., Davis, K. A., Fisher, V. A., Slopen, N., Smith, A. D. A. C., Tiemeier, H., et al. (2018) · Psychological Medicine · doi:10.1017/s0033291718000181 · Cited by 179 · see citing works
A knockoff filter for high-dimensional selective inference
Barber, R. F., & Candès, E. (2016) · Annals of Statistics · doi:10.1214/18-aos1755 · Cited by 212 · see citing works
Nadel, J., Athanasiadou, R., Lemetre, C., Wijetunga, N. A., Broin, P. Ó., Sato, H., Zhang, Z., Jeddeloh, J. A., Montagna, C., Golden, A., et al. (2015) · Epigenetics & Chromatin · doi:10.1186/s13072-015-0040-6 · Cited by 175 · see citing works
Clinical prediction from structural brain MRI scans: A large-scale empirical study
Initiative, F. T. A. D. N., Sabuncu, M. R., & Konukoglu, E. (2015) · Neuroinformatics · doi:10.1007/s12021-014-9238-1 · Cited by 161 · see citing works
The Generalized Lasso With Non-Linear Observations
Plan, Y., & Vershynin, R. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2517008 · Cited by 165 · see citing works
Sun, Z., Tao, Y., Li, S., Ferguson, K. K., Meeker, J. D., Park, S. K., Batterman, S., & Mukherjee, B. (2013) · Environmental Health · doi:10.1186/1476-069x-12-85 · Cited by 150 · see citing works
Kautzky, A., Dold, M., Bartova, L., Spies, M., Kranz, G. S., Souery, D., Montgomery, S., Mendlewicz, J., Zohar, J., Fabbri, C., et al. (2019) · Acta Psychiatrica Scandinavica · doi:10.1111/acps.12959 · Cited by 148 · see citing works
Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach
Chernozhukov, V., Hansen, C., & Spindler, M. (2015) · Annual Review of Economics · doi:10.1146/annurev-economics-012315-015826 · Cited by 149 · see citing works
Sequential Selection Procedures and False Discovery Rate Control
G’Sell, M., Wager, S., Chouldechova, A., & Tibshirani, R. J. (2015) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12122 · Cited by 141 · see citing works
Self-citationCluster analysis and prediction of residential peak demand profiles using occupant activity data
Satre-Meloy, A., Diakonova, M., & Grünewald, P. (2019) · Applied Energy · doi:10.1016/j.apenergy.2019.114246 · Cited by 140 · see citing works
Simultaneous Inference for High-Dimensional Linear Models
Zhang, X., & Cheng, G. (2016) · Journal of the American Statistical Association · doi:10.1080/01621459.2016.1166114 · Cited by 139 · see citing works
Selective inference with a randomized response
Tian, X., & Taylor, J. (2018) · The Annals of Statistics · doi:10.1214/17-aos1564 · Cited by 139 · see citing works
Self-citationAdversity exposure during sensitive periods predicts accelerated epigenetic aging in children
Marini, S., Davis, K. A., Soare, T. W., Zhu, Y., Suderman, M. J., Simpkin, A. J., Smith, A. D. A. C., Wolf, E. J., Relton, C. L., & Dunn, E. C. (2019) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2019.104484 · Cited by 140 · see citing works
Hindman, M. (2015) · The Annals of the American Academy of Political and Social Science · doi:10.1177/0002716215570279 · Cited by 139 · see citing works
Siggiridou, E., & Kugiumtzis, D. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2500893 · Cited by 131 · see citing works
How Much Does Your Data Exploration Overfit? Controlling Bias via Information Usage
Russo, D., & Zou, J. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2945779 · Cited by 226 · see citing works
Lees, J. A., Mai, T., Galardini, M., Wheeler, N. E., Horsfield, S., Parkhill, J., & Corander, J. (2020) · mBio · doi:10.1128/mbio.01344-20 · Cited by 120 · see citing works
Williams, D. R. (2021) · Multivariate Behavioral Research · doi:10.1080/00273171.2021.1894412 · Cited by 120 · see citing works
SLOPE is adaptive to unknown sparsity and asymptotically minimax
Su, W., & Candès, E. J. (2016) · The Annals of Statistics · doi:10.1214/15-aos1397 · Cited by 111 · see citing works
Electricity price forecasting using sale and purchase curves: The X-Model
Ziel, F., & Steinert, R. (2016) · Energy Economics · doi:10.1016/j.eneco.2016.08.008 · Cited by 119 · see citing works
Inference and uncertainty quantification for noisy matrix completion
Chen, Y., B, J. F. A., Ma, C., & Yan, Y. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1910053116 · Cited by 115 · see citing works
OR Forum—An Algorithmic Approach to Linear Regression
Bertsimas, D., & King, A. (2015) · Operations Research · doi:10.1287/opre.2015.1436 · Cited by 110 · see citing works
Son, Y., Osornio-Vargas, Á. R., O’Neill, M. S., Hystad, P., Texcalac-Sangrador, J. L., Ohman‐Strickland, P., Meng, Q., & Schwander, S. (2018) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2018.05.144 · Cited by 110 · see citing works
Graphical Models via Univariate Exponential Family Distributions.
Yang, E., Ravikumar, P., Allen, G. I., & Liu, Z. (2015) · PubMed · Cited by 107 · see citing works
Ramsay, I. S., Ma, S., Fisher, M., Loewy, R. L., Ragland, J. D., Niendam, T. A., Carter, C. S., & Vinogradov, S. (2017) · Schizophrenia Research Cognition · doi:10.1016/j.scog.2017.10.001 · Cited by 105 · see citing works
Hsu, D. (2015) · Energy · doi:10.1016/j.energy.2015.02.008 · Cited by 99 · see citing works
Lees, J. A., Croucher, N. J., Goldblatt, D., Nosten, F. H., Parkhill, J., Turner, C. L., Turner, P., & Bentley, S. D. (2017) · eLife · doi:10.7554/elife.26255 · Cited by 100 · see citing works
Uniform asymptotic inference and the bootstrap after model selection
Tibshirani, R. J., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018) · The Annals of Statistics · doi:10.1214/17-aos1584 · Cited by 98 · see citing works
Self-citationOnline rules for control of false discovery rate and false discovery exceedance
Javanmard, A., & Andrea Montanari, A. (2018) · The Annals of Statistics · doi:10.1214/17-aos1559 · Cited by 97 · see citing works
Salvador, R. M., Raduà, J., Canales-Rodríguez, E. J., Solanes, A., Sarró, S., Goikolea, J. M., Valiente-Gómez, A., Monté, G. C., Natividad, M. D. C., Guerrero‐Pedraza, A., et al. (2017) · PLoS ONE · doi:10.1371/journal.pone.0175683 · Cited by 95 · see citing works
Teipel, S. J., Kurth, J., Krause, B. J., & Grothe, M. J. (2015) · NeuroImage Clinical · doi:10.1016/j.nicl.2015.05.006 · Cited by 94 · see citing works
Chase, H. W., Fournier, J. C. J., Bertocci, M. A., Greenberg, T., Aslam, H. A., Stiffler, R. S., Lockovich, J., Graur, S., Bebko, G. M., Forbes, E. E., et al. (2017) · Translational Psychiatry · doi:10.1038/tp.2017.60 · Cited by 92 · see citing works
Belzak, W. C. M., & Bauer, D. J. (2020) · Psychological Methods · doi:10.1037/met0000253 · Cited by 91 · see citing works
Valid post-selection and post-regularization inference: An elementary, general approach
Chernozhukov, V., Hansen, C., & Spindler, M. (2017) · doi:10.1920/wp.cem.2016.3616 · Cited by 89 · see citing works
Regularized Ordinal Regression and the ordinalNet R Package
Wurm, M., Rathouz, P., & Hanlon, B. (2017) · Journal of Statistical Software · doi:10.18637/jss.v099.i06 · Cited by 120 · see citing works
Schneeweiß, S., Eddings, W., Glynn, R. J., Patorno, E., Rassen, J. A., & Franklin, J. M. (2016) · Epidemiology · doi:10.1097/ede.0000000000000581 · Cited by 83 · see citing works
Polygenic Analysis of Late-Onset Alzheimer’s Disease from Mainland China
Jiao, B., Liu, X., Zhou, L., Wang, M. H., Zhou, Y., Xiao, T., Zhang, W., Sun, R., Waye, M. M. Y., Tang, B., et al. (2015) · PLoS ONE · doi:10.1371/journal.pone.0144898 · Cited by 82 · see citing works
Bränn, E., Papadopoulos, F. C., Fransson, E., White, R. A., Edvinsson, Å., Hellgren, C., Kamali‐Moghaddam, M., Boström, A. E. D., Schiöth, H. B., Poromaa, I. S., et al. (2017) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2017.02.029 · Cited by 82 · see citing works
Statistical Inference, Learning and Models in Big Data
Franke, B., Plante, J., Roscher, R., Lee, E. A., Smyth, C., Hatefi, A., Chen, F., Gil, E., Schwing, A. G., Selvitella, A., et al. (2016) · International Statistical Review · doi:10.1111/insr.12176 · Cited by 80 · see citing works
Jacobucci, R., Brandmaier, A. M., & Kievit, R. (2019) · Advances in Methods and Practices in Psychological Science · doi:10.1177/2515245919826527 · Cited by 78 · see citing works
Schwarzkopf, L., Witt, S., Waelscher, J., Polke, M., & Kreuter, M. (2018) · Respiratory Research · doi:10.1186/s12931-018-0769-0 · Cited by 77 · see citing works
Bootstrapping and sample splitting for high-dimensional, assumption-lean inference
Rinaldo, A., Wasserman, L., & G’Sell, M. (2019) · The Annals of Statistics · doi:10.1214/18-aos1784 · Cited by 77 · see citing works
False Discovery Rate Control via Data Splitting
Dai, C., Lin, B., Xing, X., & Liu, J. S. (2022) · Journal of the American Statistical Association · doi:10.1080/01621459.2022.2060113 · Cited by 77 · see citing works
Nearly optimal Bayesian shrinkage for high-dimensional regression
Song, Q., & Liang, F. (2022) · Science China Mathematics · doi:10.1007/s11425-020-1912-6 · Cited by 77 · see citing works
Preventive medicine of von Hippel–Lindau disease-associated pancreatic neuroendocrine tumors
Krauß, T., Ferrara, A. M., Links, T. P., Wellner, U. F., Bancos, I., Kvacheniuk, A. N., Heras, K. V. G. D. L., Yukina, M. Y., Petrov, R., Bullivant, G., et al. (2018) · Endocrine Related Cancer · doi:10.1530/erc-18-0100 · Cited by 70 · see citing works
Some Natural Solutions to thep-Value Communication Problem—and Why They Won’t Work
Gelman, A., & Carlin, J. B. (2017) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1311263 · Cited by 68 · see citing works
Seifert, M., Peitzsch, C., Gorodetska, I., Börner, C., Klink, B., & Dubrovska, A. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007460 · Cited by 68 · see citing works
Testing and Confidence Intervals for High Dimensional Proportional Hazards Models
Fang, E. X., Ning, Y., & Liu, H. (2016) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12224 · Cited by 68 · see citing works
A Unified Theory of Confidence Regions and Testing for High-Dimensional Estimating Equations
Neykov, M., Ning, Y., Liu, J. S., & Liu, H. (2018) · Statistical Science · doi:10.1214/18-sts661 · Cited by 66 · see citing works
LassoNet: Neural Networks with Feature Sparsity.
Lemhadri, I., Ruan, F., & Tibshirani, R. J. (2021) · PubMed · Cited by 65 · see citing works
Self-citationModel Selection of the Effect of Binary Exposures over the Life Course
Smith, A. D. A. C., Heron, J., Mishra, G., Gilthorpe, M. S., Ben-Shlomo, Y., & Tilling, K. (2015) · Epidemiology · doi:10.1097/ede.0000000000000348 · Cited by 63 · see citing works
Estimation of biomass burning emissions by integrating ICESat-2, Landsat 8, and Sentinel-1 data
Liu, M., & Popescu, S. (2022) · Remote Sensing of Environment · doi:10.1016/j.rse.2022.113172 · Cited by 63 · see citing works
Predicting access to healthful food retailers with machine learning
Amin, M. D., Badruddoza, S., & McCluskey, J. J. (2020) · Food Policy · doi:10.1016/j.foodpol.2020.101985 · Cited by 62 · see citing works
Life-course exposure to air pollution and biological ageing in the Lothian Birth Cohort 1936
Baranyi, G., Deary, I. J., McCartney, D. L., Harris, S. E., Shortt, N., Reis, S., Russ, T. C., Thompson, C. W., Vieno, M., Cox, S. R., et al. (2022) · Environment International · doi:10.1016/j.envint.2022.107501 · Cited by 59 · see citing works
Two-Step Lasso Estimation of the Spatial Weights Matrix
Ahrens, A., & Bhattacharjee, A. (2015) · Econometrics · doi:10.3390/econometrics3010128 · Cited by 62 · see citing works
EigenPrism: Inference for High Dimensional Signal-to-Noise Ratios
Janson, L., Barber, R. F., & Candès, E. J. (2016) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12203 · Cited by 62 · see citing works
Network classification with applications to brain connectomics
Relión, J. D. A., Kessler, D. A., Levina, E., & Taylor, S. F. (2019) · The Annals of Applied Statistics · doi:10.1214/19-aoas1252 · Cited by 58 · see citing works
LASSO Model of Postdisaster Housing Recovery: Case Study of Hurricane Sandy
Nejat, A., & Ghosh, S. (2016) · Natural Hazards Review · doi:10.1061/(asce)nh.1527-6996.0000223 · Cited by 61 · see citing works
Topographies of Cortical and Subcortical Volume Loss in HIV and Aging in the cART Era
Guha, A., Brier, M. R., Ortega, M., Westerhaus, E. T., Nelson, B., & Ances, B. M. (2016) · JAIDS Journal of Acquired Immune Deficiency Syndromes · doi:10.1097/qai.0000000000001111 · Cited by 60 · see citing works
A structured approach to hypotheses involving continuous exposures over the life course
Smith, A. D. A. C., Hardy, R., Heron, J., Joinson, C. J., Lawlor, D. A., Macdonald-Wallis, C., & Tilling, K. (2016) · International Journal of Epidemiology · doi:10.1093/ije/dyw164 · Cited by 59 · see citing works
Comparison of weighting approaches for genetic risk scores in gene-environment interaction studies
Hüls, A., Krämer, U., Carlsten, C., Schikowski, T., Ickstadt, K., & Schwender, H. R. (2017) · BMC Genetics · doi:10.1186/s12863-017-0586-3 · Cited by 59 · see citing works
Predicting real-time surge pricing of ride-sourcing companies
Battifarano, M., & Qian, S. (2019) · Transportation Research Part C Emerging Technologies · doi:10.1016/j.trc.2019.08.019 · Cited by 59 · see citing works
Satre-Meloy, A. (2019) · Energy · doi:10.1016/j.energy.2019.01.157 · Cited by 59 · see citing works
Gross, S. M., & Tibshirani, R. (2014) · Biostatistics · doi:10.1093/biostatistics/kxu047 · Cited by 57 · see citing works
Self-citationHigh-dimensional inference in misspecified linear models
Bühlmann, P., & van de Geer, S. (2015) · Electronic Journal of Statistics · doi:10.1214/15-ejs1041 · Cited by 54 · see citing works
Too many covariates and too few cases? – a comparative study
Chen, Q., Nian, H., Zhu, Y., Talbot, H. K., Griffin, M. R., & Harrell, F. E. (2016) · Statistics in Medicine · doi:10.1002/sim.7021 · Cited by 54 · see citing works
Bootstrap Enhanced Penalized Regression for Variable Selection with Neuroimaging Data
Abram, S. V., Helwig, N. E., Moodie, C. A., DeYoung, C. G., MacDonald, A. W., & Waller, N. G. (2016) · Frontiers in Neuroscience · doi:10.3389/fnins.2016.00344 · Cited by 53 · see citing works
Panel data quantile regression with grouped fixed effects
Gu, J., & Stanislav Volgushev, A. (2019) · Journal of Econometrics · doi:10.1016/j.jeconom.2019.04.006 · Cited by 53 · see citing works
Cronin, R. M., VanHouten, J. P., Siew, E. D., Eden, S., Fihn, S. D., Nielson, C. D., Peterson, J. F., Baker, C. R., Ikizler, T. A., Speroff, T., et al. (2015) · Journal of the American Medical Informatics Association · doi:10.1093/jamia/ocv051 · Cited by 53 · see citing works
The Cluster Elastic Net for High-Dimensional Regression With Unknown Variable Grouping
Witten, D., Shojaie, A., & Zhang, F. (2013) · Technometrics · doi:10.1080/00401706.2013.810174 · Cited by 51 · see citing works
Maker, A. V., Hu, V. H., Kadkol, S. S., Hong, L. K., Brugge, W. R., Winter, J. M., Yeo, C. J., Hackert, T., Büchler, M. W., Lawlor, R. T., et al. (2019) · Journal of the American College of Surgeons · doi:10.1016/j.jamcollsurg.2019.02.040 · Cited by 52 · see citing works
Does cybersecurity risk stifle corporate innovation activities?
Wang, J., Ho, C. Y., & Shan, Y. G. (2023) · International Review of Financial Analysis · doi:10.1016/j.irfa.2023.103028 · Cited by 47 · see citing works
Sparse Estimation and Uncertainty with Application to Subgroup Analysis
Ratkovic, M., & Tingley, D. H. (2017) · Political Analysis · doi:10.1017/pan.2016.14 · Cited by 51 · see citing works
Penalized expectile regression: an alternative to penalized quantile regression
Liao, L., Park, C., & Choi, H. (2018) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-018-0645-1 · Cited by 51 · see citing works
Tests for High Dimensional Generalized Linear Models
Guo, B., & Chen, S. X. (2016) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12152 · Cited by 50 · see citing works
- Authors
- Lockhart, R., Taylor, J., Tibshirani, R. J., & Tibshirani, R.
- Affiliations
- Simon Fraser University (CA)
- Carnegie Mellon University (US)
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2014-04-01
- Volume
- 42
- Issue
- 2
- Pages
- 413-468
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- PMC
- PMC4285373
- OpenAlex
- W2172185584
- Cited by
- 541
- References
- 64
- Citations by year
- 2026: 6 · 2025: 20 · 2024: 21 · 2023: 22 · 2022: 43 · 2021: 40 · 2020: 59 · 2019: 68 · 2018: 67 · 2017: 51 · 2016: 60 · 2015: 50 · 2014: 23 · 2013: 11
- FWCI
- 64.76
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- The Annals of Statistics (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- KiltHub Repository (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- National Institutes of Health
- Natural Sciences and Engineering Research Council of Canada
- National Institute of Biomedical Imaging and Bioengineering (R01EB001988)
- Air Force Office of Scientific Research
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Keywords
- LASSO, significance testing, sparse linear regression, shrinkage, high-dimensional regression, nested models
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
