Assessing model adequacy in possibly misspecified quantile regression
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.
conditional quantiles coefficient of determination lack-of-fit linear model prediction quality