Penalized inverse probability weighted estimators for weighted rank regression with missing covariates. Issue 5 (3rd March 2016)

• Record Type: Journal Article
• Authors: Yang, Hu; Guo, Chaohui; Lv, Jing
• Is Part Of: Communications in statistics. Volume 45:Issue 5(2016)
• Page Start: 1388
• Page End: 1402
• Publication Date: 2016-03-03
• Subjects: Horvitz-Thompson property -- MAR -- Rank-based analysis -- SCAD -- Variable selection.; 62H12 -- 62J05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.863930
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this article, we study the variable selection and estimation for linear regression models with missing covariates. The proposed estimation method is almost as efficient as the popular least-squares-based estimation method for normal random errors and empirically shown to be much more efficient and robust with respect to heavy tailed errors or outliers in the responses and covariates. To achieve sparsity, a variable selection procedure based on SCAD is proposed to conduct estimation and variable selection simultaneously. The procedure is shown to possess the oracle property. To deal with the covariates missing, we consider the inverse probability weighted estimators for the linear model when the selection probability is known or unknown. It is shown that the estimator by using estimated selection probability has a smaller asymptotic variance than that with true selection probability, thus is more efficient. Therefore, the important Horvitz-Thompson property is verified for penalized rank estimator with the covariates missing in the linear model. Some numerical examples are provided to demonstrate the performance of the estimators.