Goodness-of-fit tests for quantile regression with missing responses

Goodness-of-fit tests for quantile regression models, in the presence of missing observations in the response variable, are introduced and analysed in this paper. The different proposals are based on the construction of empirical processes considering three different approaches which involve the use of the gradient vector of the quantile function, a linear projection of the covariates (suitable for high-dimensional settings) and a projection of the estimating equations. Besides, two types of estimators for the null parametric model to be tested are considered. The performance of the different test statistics is analysed in an extensive simulation study. An application to real data is also included.

Automated summary

This paper introduces and analyzes goodness-of-fit tests for quantile regression models in the presence of missing observations in the response variable, based on construction of empirical processes and considering three different approaches. The performance of different test statistics is extensively studied through simulation, with an application to real data included.