Quantile regression and variable selection for partially linear model with randomly truncated data

• Published in: Statistical papers (Berlin, Germany) Vol. 60; no. 4; pp. 1137 - 1160
• Main Authors: Xu, Hong-Xia, Chen, Zhen-Long, Wang, Jiang-Feng, Fan, Guo-Liang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2019; Springer Nature B.V
• Subjects: Computer simulation; Distribution functions; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Estimating techniques; Estimators; Finance; Insurance; Management; Mathematics and Statistics; Operations Research/Decision Theory; Parameter estimation; Probability Theory and Stochastic Processes; Regression; Regression analysis; Regular Article; Statistics; Statistics for Business; Left-truncated data; 62G05; SCAD; 62G20; Quantile regression; Oracle properties; Variable selection
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-016-0867-3

This paper focuses on the problem of estimation and variable selection for quantile regression (QR) of partially linear model (PLM) where the response is subject to random left truncation. We propose a three-stage estimation procedure for parametric and nonparametric parts based on the weights which are random quantities and determined by the product-limit estimates of the distribution function of truncated variable. The estimators obtained in the second and third stages are more efficient than the initial estimators in the first stage. Furthermore, we propose a variable selection procedure for the QR of PLM by combining the estimation method with the smoothly clipped absolute deviation penalty to get sparse estimation of the regression parameter. The oracle properties of the variable selection approach are established. Simulation studies are conducted to examine the performance of our estimators and variable selection method.