Distribution-Free Prediction Sets for Two-Layer Hierarchical Models

References

• Auguie, B. (2017). gridExtra: Miscellaneous Functions for “Grid” Graphics, R package version 2.3.
   Google Scholar
• Balkin, T., Thome, D., Sing, H., Thomas, M., Redmond, D., Wesensten, N., Williams, J., Hall, S., and Belenky, G. (2000), “Effects of Sleep Schedules on Commercial Motor Vehicle Driver Performance,” Technical report, United States. Department of Transportation. Federal Motor Carrier Safety Administration.
   Google Scholar
• Barber, R. F., Candès, E. J., Ramdas, A., and Tibshirani, R. J. (2021a), “Predictive Inference with the Jackknife+,” The Annals of Statistics, 49, 486–507. DOI: 10.1214/20-AOS1965.
   Web of Science ®Google Scholar
• Barber, R. F., Candès, E. J., Ramdas, A., and Tibshirani, R. J. (2021b), “The Limits of Distribution-Free Conditional Predictive Inference,” Information and Inference: A Journal of the IMA, 10, 455–482.
   Google Scholar
• Bates, D., Mächler, M., Bolker, B., and Walker, S. (2015), “Fitting Linear Mixed-Effects Models Using lme4,” Journal of Statistical Software, 67, 1–48. DOI: 10.18637/jss.v067.i01.
   Web of Science ®Google Scholar
• Belenky, G., Wesensten, N. J., Thorne, D. R., Thomas, M. L., Sing, H. C., Redmond, D. P., Russo, M. B., and Balkin, T. J. (2003), “Patterns of Performance Degradation and Restoration during Sleep Restriction and Subsequent Recovery: A Sleep Dose-Response Study,” Journal of Sleep Research, 12, 1–12. DOI: 10.1046/j.1365-2869.2003.00337.x.
   PubMed Web of Science ®Google Scholar
• Bengtsson, H. (2021), R.utils: Various Programming Utilities, R package version 2.11.0.
   Google Scholar
• Booth, J. G., and Hobert, J. P. (1998), “Standard Errors of Prediction in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 93, 262–272. DOI: 10.1080/01621459.1998.10474107.
   Web of Science ®Google Scholar
• Brown, C. (2018), formula.tools: Programmatic Utilities for Manipulating Formulas, Expressions, Calls, Assignments and Other R Objects, R package version 1.7.1.
   Google Scholar
• Calvin, J. A., and Sedransk, J. (1991), “Bayesian and Frequentist Predictive Inference for the Patterns of Care Studies,” Journal of the American Statistical Association, 86, 36–48. DOI: 10.1080/01621459.1991.10475002.
   Web of Science ®Google Scholar
• Chen, W., Chun, K.-J., and Barber, R. F. (2018), “Discretized Conformal Prediction for Efficient Distribution-Free Inference,” Stat, 7, e173. DOI: 10.1002/sta4.173.
   Web of Science ®Google Scholar
• Claggett, B., Xie, M., and Tian, L. (2014), “Meta-analysis with Fixed, Unknown, Study-Specific Parameters,” Journal of the American Statistical Association, 109, 1660–1671. DOI: 10.1080/01621459.2014.957288.
   Web of Science ®Google Scholar
• Csárdi, G., and FitzJohn, R. (2019), progress: Terminal Progress Bars, R package version 1.2.2.
   Google Scholar
• DerSimonian, R., and Laird, N. (1986), “Meta-Analysis in Clinical Trials,” Controlled Clinical Trials, 7, 177–188. DOI: 10.1016/0197-2456(86)90046-2.
   PubMed Web of Science ®Google Scholar
• Dowle, M., and Srinivasan, A. (2021), data.table: Extension of ‘data.frame,’ R package version 1.14.2.
   Google Scholar
• Gupta, C., Kuchibhotla, A. K., and Ramdas, A. K. (2020), “Nested Conformal Prediction and Quantile Out-of-Bag Ensemble Methods,” arXiv preprint arXiv:1910.10562v2.
   Google Scholar
• Laird, N. M., and Ware, J. H. (1982), “Random-Effects Models for Longitudinal Data,” Biometrics, 38, 963–974. DOI: 10.2307/2529876.
   PubMed Web of Science ®Google Scholar
• Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., and Wasserman, L. (2018), “Distribution-Free Predictive Inference for Regression,” Journal of the American Statistical Association, 113, 1094–1111. DOI: 10.1080/01621459.2017.1307116.
   Web of Science ®Google Scholar
• Lei, J., Robins, J., and Wasserman, L. (2013), “Distribution-Free Prediction Sets,” Journal of the American Statistical Association, 108, 278–287. DOI: 10.1080/01621459.2012.751873.
   PubMed Web of Science ®Google Scholar
• Lei, J., and Wasserman, L. (2014), “Distribution-Free Prediction Bands for Non-parametric Regression,” Journal of the Royal Statistical Society, Series B, 76, 71–96. DOI: 10.1111/rssb.12021.
   Google Scholar
• Meng, X.-L. (1994), “Posterior Predictive p-values,” The Annals of Statistics, 22, 1142–1160. DOI: 10.1214/aos/1176325622.
   Web of Science ®Google Scholar
• Nystrom, N. A., Levine, M. J., Roskies, R. Z., and Scott, J. R. (2015), “Bridges: A Uniquely Flexible HPC Resource for New Communities and Data Analytics,” in Proceedings of the 2015 XSEDE Conference: Scientific Advancements Enabled by Enhanced Cyberinfrastructure, XSEDE ’15, pp. 1–8, New York, NY: Association for Computing Machinery.
   Google Scholar
• R Core Team (2021), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rüschendorf, L. (1982), “Random Variables with Maximum Sums,” Advances in Applied Probability, 14, 623–632. DOI: 10.2307/1426677.
   Web of Science ®Google Scholar
• Sadinle, M., Lei, J., and Wasserman, L. (2018), “Least Ambiguous Set-Valued Classifiers with Bounded Error Levels,” Journal of the American Statistical Association, 114, 223–234. DOI: 10.1080/01621459.2017.1395341.
   Web of Science ®Google Scholar
• Schofield, L. S., Junker, B., Taylor, L. J., and Black, D. A. (2015), “Predictive Inference Using Latent Variables With Covariates,” Psychometrika, 80, 727–747. DOI: 10.1007/s11336-014-9415-z.
   PubMed Web of Science ®Google Scholar
• Shafer, G., and Vovk, V. (2008), “A Tutorial on Conformal Prediction,” Journal of Machine Learning Research, 9, 371–421.
   Web of Science ®Google Scholar
• Tian, J., Chen, X., Katsevich, E., Goeman, J., and Ramdas, A. (2021), “Large-Scale Simultaneous Inference under Dependence,” arXiv preprint arXiv:2102.11253.
   Google Scholar
• Towns, J., Cockerill, T., Dahan, M., Foster, I., Gaither, K., Grimshaw, A., Hazlewood, V., Lathrop, S., Lifka, D., Peterson, G. D., Roskies, R., Scott, J. R., and Wilkins-Diehr, N. (2014), “XSEDE: Accelerating Scientific Discovery,” Computing in Science & Engineering, 16, 62–74.
   Web of Science ®Google Scholar
• Vovk, V., Gammerman, A., and Shafer, G. (2005), Algorithmic Learning in a Random World, Boston: Springer.
   Google Scholar
• Vovk, V., and Wang, R. (2020), “Combining p-values via Averaging,” Biometrika, 107, 791–808. DOI: 10.1093/biomet/asaa027.
   Web of Science ®Google Scholar
• Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L. D., François, R., Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T. L., Miller, E., Bache, S. M., Müller, K., Ooms, J., Robinson, D., Seidel, D. P., Spinu, V., Takahashi, K., Vaughan, D., Wilke, C., Woo, K., and Yutani, H. (2019), “Welcome to the Tidyverse,” Journal of Open Source Software, 4, 1686. DOI: 10.21105/joss.01686.
   Google Scholar