An improved weighted expectile average estimator for the regression coefficient has been obtained based on the covariate balancing propensity score (CBPS), when the responses of linear models are missing at random. The asymptotic normality of the proposed method has been proved, and the estimation effect of the method is further illustrated by numerical simulation.

In this paper, we consider the multiple robust estimation of the parameters in the varying-coefficient partially linear model with response missing at random. The multiple robust estimation method is proposed, and the multiple robustness of the proposed method is proved. Numerical simulations are conducted to investigate the finite sample performance of the proposed estimators compared with other competitors.

In this article, two types of weighted quantile estimators were proposed for nonlinear models with missing covariates. The asymptotic normality of the proposed weighted quantile average estimators was established. We further calculated the optimal weights and derived the asymptotic distributions of the correspondingly resulted optimal weighted quantile estimators. Numerical simulations and a real data analysis were conducted to examine the finite sample performance of the proposed estimators compared with other competitors.