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Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response

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  • Zhang, Ting
  • Wang, Lei

Abstract

With nonignorable missing responses, an efficient estimator and a variable selection method for quantile regression coefficient are proposed based on smoothed weighted empirical likelihood (SWEL). To handle the identifiability issue, a part of covariates named as nonresponse instrument is used, which is related to response but unrelated to the propensity conditioned on response and other observed covariates. The generalized method of moments is applied to estimate the parameters in the nonresponse propensity. Based on inverse probability weighting and kernel smoothing approaches, consistency and asymptotic normality of the proposed estimator for quantile regression coefficient are established. The asymptotic properties of the resulting SWEL ratio function and the corresponding confidence regions are derived. Further, a penalized SWEL method and its algorithm for variable selection are investigated. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.

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  • Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302439
    DOI: 10.1016/j.csda.2019.106888
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