Cross-validating fit and predictive accuracy of nonlinear quantile regressions |
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Authors: | Harry Haupt Kathrin Kagerer Joachim Schnurbus |
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Institution: | 1. Centre for Statistics, Department of Economics and Business Administration , Bielefeld University , Germany;2. Department of Economics , University of Regensburg , Germany |
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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. |
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Keywords: | quantile regression spline kernel cross validation model selection mixed covariates |
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