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Assessing model adequacy in possibly misspecified quantile regression. (English) Zbl 1365.62143
Summary: Possibly misspecified linear quantile regression models are considered. A measure for assessing the combined effect of several covariates on a certain conditional quantile function is proposed. The measure is based on an adaptation to quantile regression of the famous coefficient of determination originally proposed for mean regression, and compares a ‘reduced’ model to a ‘full’ model, both of which can be misspecified. An estimator of this measure is proposed and its asymptotic distribution is investigated both in the non-degenerate and the degenerate case. The finite sample performance of the estimator is studied through a number of simulation experiments. The proposed measure is also applied to a data set on body fat measures.

62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
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