Cross-validating fit and predictive accuracy of nonlinear quantile regressions

Harry Haupt, Kathrin Kagerer and Joachim Schnurbus

Journal of Applied Statistics, 2011, vol. 38, issue 12, 2939-2954

Abstract: The paper proposes a cross-validation method to address the question of specification search in a multiple nonlinear quantile regression framework. Linear parametric, spline-based partially linear and kernel-based fully nonparametric specifications are contrasted as competitors using cross-validated weighted L 1 -norm based goodness-of-fit and prediction error criteria. The aim is to provide a fair comparison with respect to estimation accuracy and/or predictive ability for different semi- and nonparametric specification paradigms. This is challenging as the model dimension cannot be estimated for all competitors and the meta-parameters such as kernel bandwidths, spline knot numbers and polynomial degrees are difficult to compare. General issues of specification comparability and automated data-driven meta-parameter selection are discussed. The proposed method further allows us to assess the balance between fit and model complexity. An extensive Monte Carlo study and an application to a well-known data set provide empirical illustration of the method.

Date: 2011
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DOI: 10.1080/02664763.2011.573542

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