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Goodness-of-fit tests for quantile regression with missing responses. (English) Zbl 1477.62096

Summary: 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.

MSC:

62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62D10 Missing data
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