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. © 2012 Elsevier B.V. All rights reserved.
Noh, H., El Ghouch, A., & Van Keilegom, I. (2013). Assessing model adequacy in possibly misspecified quantile regression. Computational Statistics and Data Analysis, 57(1), 558–569. https://doi.org/10.1016/j.csda.2012.07.020