×

Variable selection in censored quantile regression with high dimensional data. (English) Zbl 1392.62115

Summary: We propose a two-step variable selection procedure for censored quantile regression with high dimensional predictors. To account for censoring data in high dimensional case, we employ effective dimension reduction and the ideas of informative subset idea. Under some regularity conditions, we show that our procedure enjoys the model selection consistency. Simulation study and real data analysis are conducted to evaluate the finite sample performance of the proposed approach.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62J07 Ridge regression; shrinkage estimators (Lasso)
62N01 Censored data models

Software:

quantreg
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alhamzawi R, Yu K, Benoit D. Bayesian adaptive lasso quantile regression. Stat Model, 2012, 12: 279-297 · Zbl 1306.65029 · doi:10.1177/1471082X1101200304
[2] Belloni A, Chernozhukov V. ℓ1-Penalized quantile regression in high dimensional sparse models. Ann Statist, 2011, 39: 82-130 · Zbl 1209.62064 · doi:10.1214/10-AOS827
[3] Bertsimas D, Tsitsiklis J. Introduction to Linear Optimization. Belmont: Athena Scientific, 1997
[4] Candes E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n. Ann Statist, 2007, 35: 2313-2351 · Zbl 1139.62019 · doi:10.1214/009053606000001523
[5] Carroll R, Fan J, Gijbels I, et al. Generalized partially linear single-index models. J Amer Statist Assoc, 1997, 92: 477-489 · Zbl 0890.62053 · doi:10.1080/01621459.1997.10474001
[6] Chen J, Chen Z. Extended Bayesian information criteria for model selection with large model space. Biometrika, 2008, 95: 759-771 · Zbl 1437.62415 · doi:10.1093/biomet/asn034
[7] Chernozhukov V, Hong H. Three-step censored quantile regression and extramarital affairs. J Amer Statist Assoc, 2002, 97: 872-882 · Zbl 1048.62112 · doi:10.1198/016214502388618663
[8] Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Amer Statist Assoc, 2001, 96: 1348-1360 · Zbl 1073.62547 · doi:10.1198/016214501753382273
[9] Fan J, Lv J. Sure independence screening for ultrahigh dimensional feature space. J Roy Statist Soc Ser B, 2008, 70: 849-911 · Zbl 1411.62187 · doi:10.1111/j.1467-9868.2008.00674.x
[10] Fan J, Song R. Sure independence screening in generalized linear models with NP-dimensionality. Ann Statist, 2010, 38: 3567-3604 · Zbl 1206.68157 · doi:10.1214/10-AOS798
[11] Fitzenberger B, Winker P. Improving the computation of censored quantile regressions. Comput Statist Data Anal, 2007, 52: 88-108 · Zbl 1452.62904 · doi:10.1016/j.csda.2007.01.013
[12] Galvao A, Lamarche C, Lima L. Estimation of censored quantile regression for panel data with fixed effects. J Amer Statist Assoc, 2013, 108: 1075-1089 · Zbl 06224988 · doi:10.1080/01621459.2013.818002
[13] Huang J, Ma S, Zhang C. Adaptive Lasso for sparse high dimensional regression models. Statist Sinica, 2008, 18: 1603-1618 · Zbl 1255.62198
[14] Koenker R. Quantile Regression. Cambridge: Cambridge University Press, 2005 · Zbl 1111.62037 · doi:10.1017/CBO9780511754098
[15] Koenker R. Censored quantile regression redux. J Statist Software, 2008, 27: 1-25 · doi:10.18637/jss.v027.i06
[16] Koenker R, Bassett G. Regression quantiles. Econometrica, 1978, 46: 33-50 · Zbl 0373.62038 · doi:10.2307/1913643
[17] Koenker R, Park B. An interior point algorithm for nonlinear quantile regression. J Econometrics, 1996, 71: 265-283 · Zbl 0855.62030 · doi:10.1016/0304-4076(96)84507-6
[18] Meinshausen N, Yu B. LASSO-type recovery of sparse representations for high dimensional data. Ann Statist, 2009, 37: 246-270 · Zbl 1155.62050 · doi:10.1214/07-AOS582
[19] Powell J. Censored regression quantiles. J Econometrics, 1986, 32: 143-155 · Zbl 0605.62139 · doi:10.1016/0304-4076(86)90016-3
[20] Scheetz T, Kim K, Swiderski R, et al. Regulation of gene expression in the mammalian eye and its relevance to eye disease. Proc Natl Acad Sci USA, 2006, 103: 14429-14434 · doi:10.1073/pnas.0602562103
[21] Tang Y, Song X,Wang H, et al. Variable selection in high dimensional quantile varying coeffcient models. J Multivariate Anal, 2013, 122: 115-132 · Zbl 1279.62049 · doi:10.1016/j.jmva.2013.07.015
[22] Tang Y, Wang H, He X, et al. An informative subset-based estimator for censored quantile regression. TEST, 2012, 21: 635-655 · Zbl 1284.62269 · doi:10.1007/s11749-011-0266-y
[23] Tibshirani R. Regression shrinkage and selection via the LASSO. J Roy Statist Soc Ser B, 1996, 58: 267-288 · Zbl 0850.62538
[24] Tobin J. Estimation of relationships for limited dependent variables. Econometrica, 1958, 26: 24-36 · Zbl 0088.36607 · doi:10.2307/1907382
[25] Volgushev S, Wagener J, Dette H. Censored quantile regression processes under dependence and penalization. Electron J Stat, 2014, 8: 2405-2447 · Zbl 1349.62488 · doi:10.1214/14-EJS54
[26] Wang H, Fygenson M. Inference for censored quantile regression models in longitudinal studies. Ann Statist, 2009, 37: 756-781 · Zbl 1162.62035 · doi:10.1214/07-AOS564
[27] Wang H, Zhou J, Li Y. Variable selection for censored quantile regression. Statist Sinica, 2013, 23: 145-167 · Zbl 1257.62046
[28] Wang L, Wu Y, Li R. Quantile regression for analyzing heterogeneity in ultra-high dimension. J Amer Statist Assoc, 2012, 107: 214-222 · Zbl 1328.62468 · doi:10.1080/01621459.2012.656014
[29] Wu Y, Liu Y. Variable selection in quantile regression. Statist Sinica, 2009, 19: 801-817 · Zbl 1166.62012
[30] Zhang C, Huang J. The sparsity and bias of the LASSO selection in high dimensional linear regression. Ann Statist, 2008, 36: 1567-1594 · Zbl 1142.62044 · doi:10.1214/07-AOS520
[31] Zou H. The adaptive LASSO and its oracle properties. J Amer Statist Assoc, 2006, 101: 1418-1429 · Zbl 1171.62326 · doi:10.1198/016214506000000735
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.