Assessing model adequacy in possibly misspecified quantile regression

  • Noh H
  • El Ghouch A
  • Van Keilegom I
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Abstract

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.

Author-supplied keywords

  • Coefficient of determination
  • Conditional quantiles
  • Lack-of-fit
  • Linear model
  • Prediction quality

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