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

A. Pérez-González, T. R. Cotos Yáñez, W. González–Manteiga, R. M. Crujeiras

Goodness–of–fit tests for quantile regression models, in the presence of missing observations in the response variable, are introduced and analyzed 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. In addition, for the three proposals, two types of estimators for the null parametric model to be tested are considered. The performance
of the different test statistics is analyzed in an extensive simulation study. An application to real data is also included.

Palabras clave: goodness–of–fit test missing data quantile regression

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