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When covariate information is collected through opinion surveys, experimental science, medical research and so on, incomplete records may result in missing information. Expectile regression is used in many fields; however, many fewer developments have been made with expectile regression for data with missing information. In this paper, we develop a weighted expectile regression approach for estimating the conditional expectile when covariates are missing at random (MAR). The asymptotic normality of the proposed weighted estimators is established. A proximal alternating direction method of multipliers (pADMM) algorithm is developed for the calculation of the weighted estimator. Simulation studies are conducted to assess the finite-sample performance of the proposed method. We illustrate the application of the method by analyzing a real data set from Beijing Olympic sports center monitoring stations.

Weighted expectile regression with covariates missing at random