[Publication Time] 2021-05-20

[Lead Author] 储昭霁

[Corresponding Author] 田茂再

[Journal] Journal of Mathematical Research with Applications

[Abstract]

The lack of covariate data is one of the hotspots of modern statistical analysis.It often appears in surveys or interviews, and becomes more complex in the presence of heavy tailed, skewed, and heteroscedastic data. In this sense, a robust quantile regression method is more concerned. This paper presents an inverse weighted quantile regression method to explore the relationship between response and covariates. This method has several advantages over the naive estimator. On the one hand, it uses all available data and the missing covariates are allowed to be heavily correlated with the response; on the other hand, the estimator is uniform and asymptotically normal at all quantile levels. The effectiveness of this method is verified by simulation. Finally, in order to illustrate the effectiveness of this method, we extend it to the more general case, multivariate case and nonparametric case.

[Keywords]

Robust quantile regression；missing covariates；selection probability；Kernel estimator；weighting method