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On asymptotically optimal confidence regions and tests for high-dimensional models
Open accessAbstract
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking dependence among tests into account. For linear models, our method is essentially the same as in Zhang and Zhang [J. R. Stat. Soc. Ser. B Stat. Methodol. 76 (2014) 217–242]: we analyze its asymptotic properties and establish its asymptotic optimality in terms of semiparametric efficiency. Our method naturally extends to generalized linear models with convex loss functions. We develop the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.
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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
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Distribution-Free Predictive Inference for Regression
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1307116 · Cited by 1,049
A significance test for the lasso
Lockhart, R., Taylor, J., Tibshirani, R. J., & Tibshirani, R. (2014) · The Annals of Statistics · doi:10.1214/13-aos1175 · Cited by 541
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 281
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 277
Debiased machine learning of conditional average treatment effects and other causal functions
Semenova, V., & Chernozhukov, V. (2021) · The Econometrics Journal · doi:10.1093/ectj/utaa027 · Cited by 167
Metadata
- Authors
- van de Geer, S., Bühlmann, P., Ritov, Y., & Dezeure, R.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2014-06-01
- Volume
- 42
- Issue
- 3
- Pages
- 1166-1202
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2078411132
- Cited by
- 822
- References
- 1
- FWCI
- 37.46
- Type
- journal article
- Language
- en
- Open access
- green
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- van de Geer, S., Bühlmann, P., Ritov, Y., & Dezeure, R. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics. https://doi.org/10.1214/14-aos1221
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