Bootstrap confidence intervals
Open accessAbstract
This article surveys bootstrap methods for producing good approximate confidence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervals $\hat{\theta} \pm z^{(\alpha)} \hat{\sigma}$, in a way that allows routine application even to very complicated problems. Both theory and examples are used to show how this is done. The first seven sections provide a heuristic overview of four bootstrap confidence interval procedures: $BC_a$, bootstrap-t , ABC and calibration. Sections 8 and 9 describe the theory behind these methods, and their close connection with the likelihood-based confidence interval theory developed by Barndorff-Nielsen, Cox and Reid and others.
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?
The 95% confidence intervals shown in Fig. 2c, d are calculated using bootstrapping and show higher error where data are sparse.
“The 95% con fi dence interval shown in Fig. 2c, d are calculated using bootstrapping 33 and shows higher error where data are sparse.”
From Experimental reaction rates constrain estimates of ozone response to calcium carbonate geoengineering (2020) · cites this paper as [33]
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
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500 · see citing works
Self-citationAn Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1993) · doi:10.1007/978-1-4899-4541-9 · Cited by 21,230 · see citing works
Self-citationBootstrap methods: another look at the jackknife
Efron, B. (1979) · The Annals of Statistics · doi:10.1214/aos/1176344552 · Cited by 17,602 · see citing works
Self-citationBootstrap Methods and their Application
Davison, A. C., & Hinkley, D. V. (1997) · doi:10.1017/cbo9780511802843 · Cited by 7,350 · see citing works
Bootstrap Methods and Their Application
Loughin, T. M., Davison, A. C., & HINKLEY, D. V. (1999) · Journal of the American Statistical Association · doi:10.2307/2669707 · Cited by 5,478 · see citing works
Better Bootstrap Confidence Intervals
Efron, B. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478410 · Cited by 3,462 · see citing works
Self-citationThe Bootstrap and Edgeworth Expansion
Hall, P. V. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-4384-7 · Cited by 2,067 · see citing works
Empirical Likelihood Ratio Confidence Intervals for a Single Functional
Owen, A. B. (1988) · Biometrika · doi:10.1093/biomet/75.2.237 · Cited by 2,042 · see citing works
The Bootstrap and Edgeworth Expansion.
Beran, R. J., & Hall, P. A. (1993) · Journal of the American Statistical Association · doi:10.2307/2290736 · Cited by 1,927 · see citing works
Empirical Likelihood Ratio Confidence Regions
Owen, A. B. (1990) · The Annals of Statistics · doi:10.1214/aos/1176347494 · Cited by 1,507 · see citing works
Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods
EFRON, B. (1981) · Biometrika · doi:10.1093/biomet/68.3.589 · Cited by 1,399 · see citing works
Self-citationParameter Orthogonality and Approximate Conditional Inference
Cox, D. R., & Reid, N. M. (1987) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1987.tb01422.x · Cited by 1,370 · see citing works
Skovgaard, I. M., & McCullagh, P. J. (1988) · Journal of the American Statistical Association · doi:10.2307/2290168 · Cited by 868 · see citing works
Theoretical Comparison of Bootstrap Confidence Intervals
Hall, P. V. (1988) · The Annals of Statistics · doi:10.1214/aos/1176350933 · Cited by 787 · see citing works
Better Bootstrap Confidence Intervals
Efron, B. (1987) · Journal of the American Statistical Association · doi:10.2307/2289144 · Cited by 718 · see citing works
Self-citationMissing Data, Imputation, and the Bootstrap
Efron, B. (1994) · Journal of the American Statistical Association · doi:10.1080/01621459.1994.10476768 · Cited by 471 · see citing works
Self-citationOn a formula for the distribution of the maximum likelihood estimator
Barndorff-Nielsen, O. E. (1983) · Biometrika · doi:10.1093/biomet/70.2.343 · Cited by 460 · see citing works
A GENERAL METHOD FOR APPROXIMATING TO THE DISTRIBUTION OF LIKELIHOOD RATIO CRITERIA
Lawley, D. N. (1956) · Biometrika · doi:10.1093/biomet/43.3-4.295 · Cited by 409 · see citing works
On the Bootstrap and Confidence Intervals
Hall, P. A. (1986) · The Annals of Statistics · doi:10.1214/aos/1176350168 · Cited by 325 · see citing works
Infereni on full or partial parameters based on the standardized signed log likelihood ratio
Barndorff-Nielsen, O. E. (1986) · Biometrika · doi:10.1093/biomet/73.2.307 · Cited by 323 · see citing works
Prepivoting to Reduce Level Error of Confidence Sets
Beran, R. J. (1987) · Biometrika · doi:10.1093/biomet/74.3.457 · Cited by 320 · see citing works
Noninformative priors for one parameter of many
Tibshirani, R. J. (1989) · Biometrika · doi:10.1093/biomet/76.3.604 · Cited by 275 · see citing works
Jackknife-After-Bootstrap Standard Errors and Influence Functions
Efron, B. (1992) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1992.tb01866.x · Cited by 223 · see citing works
Self-citationA Simple Method for the Adjustment of Profile Likelihoods
McCullagh, P. J., & Tibshirani, R. J. (1990) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1990.tb01790.x · Cited by 221 · see citing works
On Bootstrap Resampling and Iteration
HALL, P., & Martin, M. A. (1988) · Biometrika · doi:10.1093/biomet/75.4.661 · Cited by 210 · see citing works
Calibrating Confidence Coefficients
Loh, W. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478408 · Cited by 180 · see citing works
Gleser, L. J., & Hwang, J. T. (1987) · The Annals of Statistics · doi:10.1214/aos/1176350597 · Cited by 163 · see citing works
Saddlepoint Approximations in Resampling Methods
Davison, A. C., & HINKLEY, D. V. (1988) · Biometrika · doi:10.1093/biomet/75.3.417 · Cited by 156 · see citing works
Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families
Pierce, D. A., & Peters, D. (1992) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1992.tb01445.x · Cited by 146 · see citing works
Inference on Means Using the Bootstrap
Babu, G. J., & Singh, K. (1983) · The Annals of Statistics · doi:10.1214/aos/1176346267 · Cited by 129 · see citing works
On Confidence Points and Bayesian Probability Points in the Case of Several Parameters
Peers, H. W. (1965) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1965.tb00581.x · Cited by 128 · see citing works
Bayes and likelihood calculations from confidence intervals
Efron, B. (1993) · Biometrika · doi:10.1093/biomet/80.1.3 · Cited by 120 · see citing works
Self-citationMore accurate confidence intervals in exponential families
DiCiccio, T. J., & Efron, B. (1992) · Biometrika · doi:10.1093/biomet/79.2.231 · Cited by 110 · see citing works
Self-citationSaddlepoint approximation for the studentized mean, with an application to the bootstrap
Daniels, H. E., & YOUNG, G. A. (1991) · Biometrika · doi:10.1093/biomet/78.1.169 · Cited by 86 · see citing works
Simple Modifications for Signed Roots of Likelihood Ratio Statistics
DiCiccio, T. J., & Martin, M. A. (1993) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1993.tb01485.x · Cited by 84 · see citing works
Self-citationVariance stabilization and the bootstrap
Tibshirani, R. J. (1988) · Biometrika · doi:10.1093/biomet/75.3.433 · Cited by 82 · see citing works
Missing Data, Imputation, and the Bootstrap
Efron, B. (1994) · Journal of the American Statistical Association · doi:10.2307/2290846 · Cited by 78 · see citing works
Self-citationParametrizations of Non-Linear Models
Hougaard, P. (1982) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1982.tb01205.x · Cited by 72 · see citing works
Maximum likelihood in small samples: Estimation in the presence of nuisance parameters
Sprott, D. A. (1980) · Biometrika · doi:10.1093/biomet/67.3.515 · Cited by 67 · see citing works
Adjusted Versions of Profile Likelihood and Directed Likelihood, and Extended Likelihood
Barndorff-Nielsen, O. E. (1994) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1994.tb01965.x · Cited by 58 · see citing works
On parameter transformations and interval estimation
DiCiccio, T. J. (1984) · Biometrika · doi:10.1093/biomet/71.3.477 · Cited by 49 · see citing works
Self-citationMcCullagh, P. J. (1984) · Biometrika · doi:10.1093/biomet/71.2.233 · Cited by 49 · see citing works
Fast and accurate approximate double bootstrap confidence intervals
DiCiccio, T. J., Martin, M. A., & YOUNG, G. A. (1992) · Biometrika · doi:10.1093/biomet/79.2.285 · Cited by 45 · see citing works
Self-citationCalibrating Confidence Coefficients
Loh, W. (1987) · Journal of the American Statistical Association · doi:10.2307/2289142 · Cited by 45 · see citing works
Asymptotic Iterated Bootstrap Confidence Intervals
Lee, S. M. S., & YOUNG, G. A. (1995) · The Annals of Statistics · doi:10.1214/aos/1176324710 · Cited by 43 · see citing works
Stable and invariant adjusted directed likelihoods
Barndorff-Nielsen, O. E., & Chamberlin, S. R. (1994) · Biometrika · doi:10.1093/biomet/81.3.485 · Cited by 41 · see citing works
A Note on the Calculation of Adjusted Profile Likelihood
Cox, D., & Reid, N. M. (1993) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1993.tb01916.x · Cited by 41 · see citing works
Estimation of Normal Means: Frequentist Estimation of Loss
Lu, K.-L., & Berger, J. O. (1989) · The Annals of Statistics · doi:10.1214/aos/1176347149 · Cited by 40 · see citing works
Davison, A. C., HINKLEY, D. V., & Worton, B. J. (1992) · Biometrika · doi:10.1093/biomet/79.1.113 · Cited by 33 · see citing works
Similar tests and the standardized log likelihood ratio statistic
Jensen, J. L. (1986) · Biometrika · doi:10.1093/biomet/73.3.567 · Cited by 26 · see citing works
Uniform Coverage Bounds for Confidence Intervals and Berry-Esseen Theorems for Edgeworth Expansion
Hall, P. A., & Jing, B. (1995) · The Annals of Statistics · doi:10.1214/aos/1176324525 · Cited by 22 · see citing works
Analytical approximations for iterated bootstrap confidence intervals
DiCiccio, T. J., Martin, M. A., & YOUNG, G. A. (1992) · Statistics and Computing · doi:10.1007/bf01891208 · Cited by 16 · see citing works
Self-citationOn Bootstrap Iteration for Coverage Correction in Confidence Intervals
Martin, M. A. (1990) · Journal of the American Statistical Association · doi:10.2307/2289608 · Cited by 16 · see citing works
Missing Data, Imputation, and the Bootstrap: Rejoinder
Efron, B. (1994) · Journal of the American Statistical Association · doi:10.2307/2290848 · Cited by 12 · see citing works
Self-citationBetter Boostrap Confidence Intervals: Comment
Bickel, P. J. (1987) · Journal of the American Statistical Association · doi:10.2307/2289149 · Cited by 5 · see citing works
Discussion: Theoretical Comparison of Bootstrap Confidence Intervals
Bickel, P. J. (1988) · The Annals of Statistics · doi:10.1214/aos/1176350936 · Cited by 3 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Common Beliefs and Reality About PLS: Comments on Rönkkö and Evermann (2013)
Henseler, J., Dijkstra, T. K., Sarstedt, M., Ringle, C. M., Diamantopoulos, A., Straub, D. W., Ketchen, D. J., Hair, J. F., Hult, G. T. M., & Calantone, R. J. (2014) · Organizational Research Methods · doi:10.1177/1094428114526928 · Cited by 3,332 · see citing works
Advantages of Monte Carlo confidence intervals for indirect effects
Preacher, K. J., & Selig, J. P. (2012) · Communication Methods and Measures · doi:10.1080/19312458.2012.679848 · Cited by 1,908 · see citing works
Kather, J. N., Pearson, A. T., Halama, N., Jäger, D., Krause, J., Loosen, S. H., Marx, A., Boor, P., Tacke, F., Neumann, U. P., et al. (2019) · Nature Medicine · doi:10.1038/s41591-019-0462-y · Cited by 1,458 · see citing works
Elmer, T., Mepham, K., & Stadtfeld, C. (2020) · PLOS ONE · doi:10.1371/journal.pone.0236337 · Cited by 1,421 · see citing works
“To obtain confidence intervals evaluating statistical significance, we apply bootstrapping [35] in the following way: For each number of overlapping dimensions, we sample (with PLOS ONE Students under lockdown”
MethodPupil fluctuations track rapid changes in adrenergic and cholinergic activity in cortex
Reimer, J., McGinley, M. J., Liu, Y., Rodenkirch, C., Wang, Q., McCormick, D. A., & Tolias, A. S. (2016) · Nature Communications · doi:10.1038/ncomms13289 · Cited by 926 · see citing works
Diversity and clonal selection in the human T-cell repertoire
Qi, Q., Liu, Y., Cheng, Y., Glanville, J., Zhang, D., Lee, J.-Y., Olshen, R. A., Weyand, C. M., Boyd, S. D., & Goronzy, J. J. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1409155111 · Cited by 755 · see citing works
Optogenetic inhibition of behavior with anion channelrhodopsins
Mohammad, F., Stewart, J. C., Ott, S., Chlebikova, K., Chua, J. Y., Koh, T.-W., Ho, J., & Claridge-Chang, A. (2017) · Nature Methods · doi:10.1038/nmeth.4148 · Cited by 276 · see citing works
Estimation of the relative excess risk due to interaction and associated confidence bounds
Richardson, D. B., & Kaufman, J. S. (2009) · American Journal of Epidemiology · doi:10.1093/aje/kwn411 · Cited by 240 · see citing works
Ferrario, M., Chiodini, P., Chambless, L. E., Cesana, G., Vanuzzo, D., Panico, S., Sega, R., Pilotto, L., Palmieri, L., & Giampaoli, S. (2005) · International Journal of Epidemiology · doi:10.1093/ije/dyh405 · Cited by 214 · see citing works
Alexithymia and interpersonal problems
Vanheule, S., Desmet, M., Meganck, R., & Bogaerts, S. (2007) · Journal of Clinical Psychology · doi:10.1002/jclp.20324 · Cited by 243 · see citing works
Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems
Joshi, M., Seidel-Morgenstern, A., & Kremling, A. (2006) · Metabolic Engineering · doi:10.1016/j.ymben.2006.04.003 · Cited by 190 · see citing works
Evolution pathways of IgE responses to grass and mite allergens throughout childhood
Custovic, A., Sonntag, H.-J., Buchan, I. E., Belgrave, D., Simpson, A., & Prosperi, M. C. F. (2015) · Journal of Allergy and Clinical Immunology · doi:10.1016/j.jaci.2015.03.041 · Cited by 159 · see citing works
The brain matures with stronger functional connectivity and decreased randomness of its network
Smit, D. J. A., Boersma, M., Schnack, H. G., Micheloyannis, S., Boomsma, D. I., Hulshoff Pol, H. E., Stam, C. J., & de Geus, E. J. C. (2012) · PLoS ONE · doi:10.1371/journal.pone.0036896 · Cited by 143 · see citing works
Sulis, G., Daniels, B., Kwan, A., Gandra, S., Daftary, A., Das, J., & Pai, M. (2020) · BMJ Global Health · doi:10.1136/bmjgh-2020-003393 · Cited by 132 · see citing works
Ma, J., Rosas, L. G., Lv, N., Xiao, L., Snowden, M. B., Venditti, E. M., Lewis, M. A., Goldhaber-Fiebert, J. D., & Lavori, P. W. (2019) · JAMA · doi:10.1001/jama.2019.0557 · Cited by 133 · see citing works
NREM2 and sleep spindles are instrumental to the consolidation of motor sequence memories
Laventure, S., Fogel, S., Lungu, O., Albouy, G., Sévigny-Dupont, P., Vien, C., Sayour, C., Carrier, J., Benali, H., & Doyon, J. (2016) · PLoS Biology · doi:10.1371/journal.pbio.1002429 · Cited by 132 · see citing works
Parameter uncertainty in biochemical models described by ordinary differential equations
Vanlier, J., Tiemann, C. A., Hilbers, P. A. J., & van Riel, N. A. W. (2013) · Mathematical Biosciences · doi:10.1016/j.mbs.2013.03.006 · Cited by 116 · see citing works
Iacucci, M., Daperno, M., Lazarev, M., Arsenascu, R., Tontini, G. E., Akinola, O., Gui, X. S., Villanacci, V., Goetz, M., Lowerison, M., et al. (2017) · Gastrointestinal Endoscopy · doi:10.1016/j.gie.2017.03.012 · Cited by 92 · see citing works
Panigrahy, A., Schmithorst, V. J., Wisnowski, J. L., Watson, C. G., Bellinger, D. C., Newburger, J. W., & Rivkin, M. J. (2015) · NeuroImage: Clinical · doi:10.1016/j.nicl.2015.01.013 · Cited by 86 · see citing works
Effects of compassion meditation on a psychological model of charitable donation.
Ashar, Y. K., Andrews-Hanna, J. R., Yarkoni, T., Sills, J., Halifax, J., Dimidjian, S., & Wager, T. D. (2016) · Emotion · doi:10.1037/emo0000119 · Cited by 78 · see citing works
McKeage, M. J., Kotasek, D., Markman, B., Hidalgo, M., Millward, M. J., Jameson, M. B., Harris, D. L., Stagg, R. J., Kapoun, A. M., Xu, L., et al. (2018) · Targeted Oncology · doi:10.1007/s11523-017-0543-0 · Cited by 74 · see citing works
Briere, J., Runtz, M., Eadie, E., Bigras, N., & Godbout, N. (2017) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2017.02.036 · Cited by 71 · see citing works
Receiving Post-Conflict Affiliation from the Enemy's Friend Reconciles Former Opponents
Wittig, R. M., & Boesch, C. (2010) · PLoS ONE · doi:10.1371/journal.pone.0013995 · Cited by 64 · see citing works
Explorations in statistics: the bootstrap
Curran-Everett, D. (2009) · Advances in Physiology Education · doi:10.1152/advan.00062.2009 · Cited by 52 · see citing works
Untangling serially dependent underreported count data for gender-based violence
Fernández‐Fontelo, A., Cabaña, A., Joe, H., Puig, P., & Moriña, D. (2019) · Statistics in Medicine · doi:10.1002/sim.8306 · Cited by 47 · see citing works
A feed-forward loop guarantees robust behavior in <i>Escherichia coli</i> carbohydrate uptake
Kremling, A., Bettenbrock, K., & Gilles, E. D. (2008) · Bioinformatics · doi:10.1093/bioinformatics/btn010 · Cited by 45 · see citing works
Ma, J., Yank, V., Lv, N., Goldhaber-Fiebert, J. D., Lewis, M. A., Kramer, M. K., Snowden, M. B., Rosas, L. G., Xiao, L., & Blonstein, A. C. (2015) · Contemporary Clinical Trials · doi:10.1016/j.cct.2015.06.010 · Cited by 45 · see citing works
Relationship Patterns in Alexithymia: A Study Using the Core Conflictual Relationship Theme Method
Vanheule, S., Desmet, M., Rosseel, Y., Verhaeghe, P., & Meganck, R. (2007) · Psychopathology · doi:10.1159/000096385 · Cited by 38 · see citing works
Stress-related emotional and behavioural impact following the first COVID-19 outbreak peak
Benjamin, A., Kuperman, Y., Eren, N., Rotkopf, R., Amitai, M., Rossman, H., Shilo, S., Meir, T., Keshet, A., Nuttman-Shwartz, O., et al. (2021) · Molecular Psychiatry · doi:10.1038/s41380-021-01219-6 · Cited by 33 · see citing works
Hasin, D., Shmulewitz, D., Stohl, M., Greenstein, E., Roncone, S., Aharonovich, E., & Wall, M. (2020) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2020.108294 · Cited by 31 · see citing works
Addo, O. Y., Mei, Z., Hod, E. A., Jefferds, M. E., Sharma, A. J., Flores-Ayala, R. C., Spitalnik, S. L., & Brittenham, G. M. (2022) · Blood Advances · doi:10.1182/bloodadvances.2022007066 · Cited by 32 · see citing works
Renal transplant patient acceptance of a self-management support system
Wang, W., van Lint, C. L., Brinkman, W.-P., Rövekamp, T. J. M., van Dijk, S., van der Boog, P. J. M., & Neerincx, M. A. (2017) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-017-0456-y · Cited by 30 · see citing works
Dai, Z., Weisenstein, D. K., Keutsch, F. N., & Keith, D. W. (2020) · Communications Earth & Environment · doi:10.1038/s43247-020-00058-7 · Cited by 28 · see citing works
Causal mediation analysis with a latent mediator
Albert, J. M., Geng, C., & Nelson, S. (2016) · Biometrical Journal · doi:10.1002/bimj.201400124 · Cited by 26 · see citing works
Short-term forecasts of expected deaths
Rizzi, S., & Vaupel, J. W. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2025324118 · Cited by 18 · see citing works
Mei, Z., Addo, O. Y., Jefferds, M. E. D., Flores-Ayala, R. C., & Brittenham, G. M. (2024) · Blood Advances · doi:10.1182/bloodadvances.2024013460 · Cited by 16 · see citing works
Cross-Device Federated Learning for Mobile Health Diagnostics: A First Study on COVID-19 Detection
Xia, T., Han, J., Ghosh, A., & Mascolo, C. (2023) · ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) · doi:10.1109/icassp49357.2023.10096427 · Cited by 14 · see citing works
Refaey, M. M., Al-Otibi, F. O., El-Khateeb, A. Y., Helmy, Y. A., Saber, W. I. A., & Zalma, S. A. (2024) · Scientific Reports · doi:10.1038/s41598-024-71190-z · Cited by 8 · see citing works
Detecting Data Contamination from Reinforcement Learning Post-training for Large Language Models
Tao, Y., Wang, T., Dong, Y., Liu, H., Zhang, K., Hu, X., & Li, G. (2025) · arXiv · doi:10.48550/arxiv.2510.09259 · Cited by 1 · see citing works
Factors associated with postpartum depression symptoms following antepartum hospitalization
Goulding, A. N., Palacios, D., Aras, S., Chen, H., Pasupuleti, S., Toscano, M., Cirino, N., Christie, I. C., Liu, Z., Miller, E. S., et al. (2026) · Pregnancy · doi:10.1002/pmf2.70319
“Confidence intervals (CIs) were therefore estimated using nonparametric boot-strapping with 500 resamples, which is well-established as sufficient for stable standard error estimation at our sample size, and statistical significance was assessed using the normal approximation method [39, 40].”
What Makes In-Context Examples Effective for Code Generation?
Li, D., Chen, S., Cao, J., & Cheung, S.-C. (2026) · Proceedings of the ACM on Software Engineering · doi:10.1145/3832275
- Authors
- DiCiccio, T. J., & Efron, B.
- Affiliations
- Cornell University (US)
- Stanford University (US)
- ORCID
- DiCiccio, Thomas J.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 1996-09-01
- Volume
- 11
- Issue
- 3
- Pages
- 189-228
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W1507985183
- Cited by
- 2,286
- References
- 56
- Citations by year
- 2026: 155 · 2025: 164 · 2024: 161 · 2023: 154 · 2022: 178 · 2021: 173 · 2020: 139 · 2019: 108 · 2018: 117 · 2017: 103 · 2016: 91 · 2015: 108 · 2014: 88 · 2013: 80 · 2012: 77
- FWCI
- 12.16
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Science (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Funders
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- bootstrap confidence intervals, calibration intervals, statistical inference
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
