Robust variable selection for ultrahigh-dimensional linear models with nonignorable missing response

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Abstract

We have proposed a robust and efficient variable selection method for ultrahigh-dimensional linear models with nonrandomly missing responses, leveraging modal regression. The propensity score function was specified by a semiparametric model and we introduced a two-step estimation procedure. In the first feature screening stage, the Pearson chi-square (PC) test statistic identifies significant predictors in the sparse propensity score model. The generalized method of moment (GMM) estimates parameters to obtain consistent estimation for the propensity score in the second stage. With the estimated propensity score, we suggested a feature screening and variable selection procedure based on the inverse probability weighting (IPW). A modified sure independence screening (SIS) method first reduces the model dimensionality, followed by a penalized modal regression approach to select significant covariates. The proposed procedure can deal with the ultrahigh-dimensional data with nonignorable nonresponse, and this modal-based procedure is robust against outliers and heavy-tailed errors. Additionally, we established the asymptotic properties of the estimators under mild regularity conditions. Simulation studies and real data applications confirm the method’s effectiveness in finite samples and practical settings.

Keywords

variable selection / ultrahigh-dimensional data / nonignorable missing response / modal regression / inverse probability weighting

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References

[1] R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. B, 58 (1996), 267-288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x

[2] J. Fan, R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Stat. Assoc., 96 (2001), 1348-1360. https://doi.org/10.1198/016214501753382273

[3] H. Zou, The adaptive lasso and its oracle properties, J. Am. Stat. Assoc., 101 (2006), 1418-1429. https://doi.org/10.1198/016214506000000735

[4] H. Zou, T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. B, 67 (2005), 301-320. https://doi.org/10.1111/j.1467-9868.2005.00503.x

[5] C. Zhang, Nearly unbiased variable selection under minimax concave penalty, Ann. Statist., 38 (2010), 894-942. https://doi.org/10.1214/09-AOS729

[6] J. Fan, J. Lv, Sure independence screening for ultra-high dimensional feature space, J. R. Stat. Soc. B, 70 (2008), 849-911. https://doi.org/10.1111/j.1467-9868.2008.00674.x

[7] J. Fan, R. Song, Sure independence screening in generalized linear models with NP-dimensionality, Ann. Statist., 38 (2010), 3567-3604. https://doi.org/10.1214/10-AOS798

[8] J. Fan, Y. Feng, R. Song, Nonparametric independence screening in sparse ultra-high-dimensional additive models, J. Am. Stat. Assoc., 106 (2011), 544-557. https://doi.org/10.1198/jasa.2011.tm09779

[9] J. Fan, Y. Ma, W. Dai, Nonparametric independence screening in sparse ultra-high-dimensional varying coefficient models, J. Am. Stat. Assoc., 109 (2014), 1270-1284. https://doi.org/10.1080/01621459.2013.879828

[10] H. Liang, H. Wang, C. Tsai, Profiled forward regression for ultrahigh dimensional variable screening in semiparametric partially linear models, Stat. Sin., 22 (2012), 531-554. https://doi.org/10.2139/ssrn.1746315

[11] L. Zhu, L. Li, R. Li, L. Zhu, Model-free feature screening for ultrahigh-dimensional data, J. Am. Stat. Assoc., 106 (2011), 1464-1475. https://doi.org/10.1198/jasa.2011.tm10563

[12] R. Li, W. Zhong, L. Zhu, Feature screening via distance correlation learning, J. R. Stat. Soc. B, 107 (2012), 1129-1139. https://doi.org/10.1080/01621459.2012.695654

[13] G. Li, H. Peng, J. Zhang, L. Zhu, Robust rank correlation based screening, Ann. Statist., 40 (2012), 1846-1877. https://doi.org/10.1214/12-AOS1024

[14] R. Little, D Rubin, Statistical Analysis with Missing Data, 2^nd edition , New York, 2002. https://doi.org/10.1002/9781119013563

[15] P. Zhao, L. Xue, Variable selection for semiparametric varying-coefficient partially linear models with missing response at random, Acta Math. Sin. Engl. Ser., 27 (2011), 2205-2216. https://doi.org/10.1007/s10114-011-9200-1

[16] B. Sherwood, Variable selection for additive partial linear quantile regression with missing covariates, J. Multivar. Anal., 152 (2016), 206-223. https://doi.org/10.1016/j.jmva.2016.08.009

[17] Y. Wang, Y. Song, Variable selection via penalized quasi-maximum likelihood method for spatial autoregressive model with missing response, Spat. Stat., 59 (2024), 100809. https://doi.org/10.1016/j.spasta.2023.100809

[18] P. Lai, Y. Liu, Z. Liu, Y. Wan, Model free feature screening for ultrahigh dimensional data with responses missing at random, Comput. Stat. Data Anal., 105 (2017), 201-216. https://doi.org/10.1016/j.csda.2016.08.008

[19] N. Tang, L. Xia, X. Yan, Feature screening in ultrahigh-dimensional partially linear models with missing responses at random, Comput. Stat. Data Anal., 133 (2019), 208-227. https://doi.org/10.1016/j.csda.2018.10.003

[20] X. Li, N. Tang, J. Xie, X. Yan, A nonparametric feature screening method for ultrahigh-dimensional missing response, Comput. Stat. Data Anal., 142 (2020), 106828. https://doi.org/10.1016/j.csda.2019.106828

[21] J. Kim, C. Yu, A semiparametric estimation of mean functionals with nonignorable missing data, J. Am. Stat. Assoc., 106 (2011), 157-165. https://doi.org/10.1198/jasa.2011.tm10104

[22] S. Wang, J. Shao, J. Kim, An instrumental variable approach for identification and estimation with nonignorable nonresponse, Stat. Sin., 24 (2014), 1097-1116. https://doi.org/10.5705/ss.2012.074

[23] J. Shao, L. Wang, Semiparametric inverse propensity weighting for nonignorable missing data, Biometrika, 103 (2016), 175-187. https://doi.org/10.1093/biomet/asv071

[24] N. Tang, Y. Ju, Statistical inference for nonignorable missing-data problems: a selective review, Stat. Theory Relat. Fields, 2 (2018), 105-133. https://doi.org/10.1080/24754269.2018.1522481

[25] D. Huang, R. Li, H. Wang, Feature screening for ultrahigh dimensional categorical data with applications, J. Bus. Econ. Stat., 32 (2014), 237-244. https://doi.org/10.1080/07350015.2013.863158

[26] W. Yao, B. Lindsay, R. Li, Local modal regression, J. Nonparametr. Stat., 24 (2012), 647-663. https://doi.org/10.1080/10485252.2012.678848

[27] J. Li, S. Ray, B. G. Lindsay, A nonparametric statistical approach to clustering via mode identification, J. Mach. Learn. Res., 8 (2007), 1687-1723. https://doi.org/10.5555/1314498.1314541

[28] T. Zhou, L. Zhu, Model-free feature screening for ultrahigh dimensional censored regression, Stat. Comput., 27 (2017), 947-961. https://doi.org/10.1007/s11222-016-9664-z