Variable selection for high-dimensional incomplete data using horseshoe estimation with data augmentation

References

• Bartlett, J. W., S. R. Seaman, I. R. White, and J. R. Carpenter. 2015. Multiple imputation of covariates by fully conditional specification: Accommodating the substantive model. Statistical Methods in Medical Research 24 (4):462–87. doi: 10.1177/0962280214521348.
   PubMed Web of Science ®Google Scholar
• Beesley, L. J., and J. M. Taylor. 2021. Bayesian variable selection and shrinkage strategies in a complicated modelling setting with missing data: A case study using multistate models. Statistical Modelling 21 (1–2):11–29. doi: 10.1177/1471082X20920972.
   Web of Science ®Google Scholar
• Bhattacharya, A., A. Chakraborty, and B. K. Mallick. 2016. Fast sampling with Gaussian scale-mixture priors in high-dimensional regression. Biometrika 103 (4):985–91. doi: 10.1093/biomet/asw042.
   PubMed Web of Science ®Google Scholar
• Carvalho, C. M., N. G. Polson, and J. G. Scott. 2009. Handling Sparsity via the Horseshoe. Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research. https://proceedings.mlr.press/v5/carvalho09a.html.
   Google Scholar
• Carvalho, C. M., N. G. Polson, and J. G. Scott. 2010. The horseshoe estimator for sparse signals. Biometrika 97 (2):465–80. doi: 10.1093/biomet/asq017.
   Web of Science ®Google Scholar
• Dezeure, R., P. Bühlmann, L. Meier, and N. Meinshausen. 2015. High-dimensional Inference: Confidence intervals, p-values and R-software hdi. Statistical Science 30 (4):533–58, 26. doi: 10.1214/15-STS527.
   Web of Science ®Google Scholar
• Garcia, R. I., J. G. Ibrahim, and H. Zhu. 2010. Variable selection for regression models with missing data. Statistica Sinica 20 (1):149–65.
   PubMed Web of Science ®Google Scholar
• George, E. I., and R. E. McCulloch. 1993. Variable selection via Gibbs sampling. Journal of the American Statistical Association 88 (423):881–9. doi: 10.1080/01621459.1993.10476353.
   Web of Science ®Google Scholar
• Kim, S., C. A. Sugar, and T. R. Belin. 2015. Evaluating model-based imputation methods for missing covariates in regression models with interactions. Statistics in Medicine 34 (11):1876–88. doi: 10.1002/sim.6435.
   PubMed Web of Science ®Google Scholar
• Lederer, J., and C. L. Müller. 2015. Don’t fall for tuning parameters: Tuning-free variable selection in high dimensions with the TREX. Proceedings of the AAAI Conference on Artificial Intelligence 29 (1):2729–35. https://ojs.aaai.org/index.php/AAAI/article/view/9550. doi: 10.1609/aaai.v29i1.9550.
   Google Scholar
• Lee, J. M., S. Zhang, S. Saha, S. Santa Anna, C. Jiang, and J. Perkins. 2001. RNA expression analysis using an antisense Bacillus subtilis genome array. Journal of Bacteriology 183 (24):7371–80. doi: 10.1128/JB.183.24.7371-7380.2001.
   PubMed Web of Science ®Google Scholar
• Li, Y., B. A. Craig, and A. Bhadra. 2019. The graphical horseshoe estimator for inverse covariance matrices. Journal of Computational and Graphical Statistics 28 (3):747–57. doi: 10.1080/10618600.2019.1575744.
   Web of Science ®Google Scholar
• Liang, F., B. Jia, J. Xue, Q. Li, and Y. Luo. 2018. An imputation-regularized optimization algorithm for high dimensional missing data problems and beyond. Journal of the Royal Statistical Society. Series B, Statistical Methodology 80 (5):899–926. doi: 10.1111/rssb.12279.
   PubMed Web of Science ®Google Scholar
• Liu, Y., Y. Wang, Y. Feng, and M. M. Wall. 2016. Variable selection and prediction with incomplete high-dimensional data. The Annals of Applied Statistics 10 (1):418–50. doi: 10.1214/15-AOAS899.
   PubMed Web of Science ®Google Scholar
• Long, Q., and B. A. Johnson. 2015. Variable selection in the presence of missing data: Resampling and imputation. Biostatistics (Oxford, England) 16 (3):596–610. doi: 10.1093/biostatistics/kxv003.
   PubMed Web of Science ®Google Scholar
• Maathuis, M. H., M. Kalisch, and P. Bühlmann. 2009. Estimating high-dimensional intervention effects from observational data. The Annals of Statistics 37 (6A):3133–64, 32. doi: 10.1214/09-AOS685.
   Web of Science ®Google Scholar
• Makalic, E., and D. F. Schmidt. 2016. A simple sampler for the horseshoe estimator. IEEE Signal Processing Letters 23 (1):179–82. doi: 10.1109/LSP.2015.2503725.
   Web of Science ®Google Scholar
• Matthews, B. W. 1975. Comparison of the predicted and observed secondary structure of T4 phage lysozyme. Biochimica et Biophysica Acta 405 (2):442–51. doi: 10.1016/0005-2795(75)90109-9.
   PubMed Web of Science ®Google Scholar
• Piironen, J., and A. Vehtari. 2017. Sparsity information and regularization in the horseshoe and other shrinkage priors. Electronic Journal of Statistics 11 (2):5018–51, 34. doi: 10.1214/17-EJS1337SI.
   Web of Science ®Google Scholar
• Rubin, D. B. 2004. Vol. 81 of Multiple imputation for nonresponse in surveys. United States: John Wiley & Sons.
   Google Scholar
• Rubin, D. B. 1976. Inference and missing data. Biometrika 63 (3):581–92. doi: 10.1093/biomet/63.3.581.
   Web of Science ®Google Scholar
• Rue, H. 2001. Fast sampling of Gaussian Markov random fields. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (2):325–38. doi: 10.1111/1467-9868.00288.
   Google Scholar
• Schafer, J. L. 1997. Analysis of incomplete multivariate data. New York, NY: CRC Press.
   Google Scholar
• Tanner, M. A., and W. H. Wong. 1987. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82 (398):528–40. doi: 10.1080/01621459.1987.10478458.
   Web of Science ®Google Scholar
• Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 (1):267–88.
   Web of Science ®Google Scholar
• van Dyk, D. A., and X.-L. Meng. 2001. The art of data augmentation. Journal of Computational and Graphical Statistics 10 (1):1–50. doi: 10.1198/10618600152418584.
   Web of Science ®Google Scholar
• Wand, M. P., J. T. Ormerod, S. A. Padoan, and R. Frühwirth. 2011. Mean field variational bayes for elaborate distributions. Bayesian Analysis 6 (4):847–900. doi: 10.1214/11-BA631.
   Web of Science ®Google Scholar
• World Bank Group. 2021. The world bank data. Accessed May 8, 2021. http://data.worldbank.org.
   Google Scholar
• Yang, X., T. R. Belin, and W. J. Boscardin. 2005. Imputation and variable selection in linear regression models with missing covariates. Biometrics 61 (2):498–506. doi: 10.1111/j.1541-0420.2005.00317.x.
   PubMed Web of Science ®Google Scholar