Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses

Xianwen Ding, Jiandong Chen and Xueping Chen ()
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Xianwen Ding: Jiangsu University of Technology
Jiandong Chen: Jiangsu University of Technology
Xueping Chen: Jiangsu University of Technology

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 5, No 2, 545-568

Abstract: Abstract The paper concerns the regularized quantile regression for ultrahigh-dimensional data with responses missing not at random. The propensity score is specified by the semiparametric exponential tilting model. We use the Pearson Chi-square type test statistic for identification of the important features in the sparse propensity score model, and employ the adjusted empirical likelihood method for estimation of the parameters in the reduced model. With the estimated propensity score model, we suggest an inverse probability weighted and penalized objective function for regularized estimation using the nonconvex SCAD penalty and MCP functions. Assuming the propensity score model is of low dimension, we establish the oracle properties of the proposed regularized estimators. The new method has several desirable advantages. First, it is robust to heavy-tailed errors or potential outliers in the responses. Second, it can accommodate nonignorable nonresponse data. Third, it can deal with ultrahigh-dimensional data with heterogeneity. Simulation study and real data analysis are given to examine the finite sample performance of the proposed approaches.

Keywords: Quantile regression; Regularized estimation; Missing not at random; Inverse probability weighting; Pearson Chi-square test (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-019-00744-3

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