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Cross-validating fit and predictive accuracy of nonlinear quantile regressions

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  • Harry Haupt
  • Kathrin Kagerer
  • Joachim Schnurbus

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.

Suggested Citation

  • Harry Haupt & Kathrin Kagerer & Joachim Schnurbus, 2011. "Cross-validating fit and predictive accuracy of nonlinear quantile regressions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2939-2954, March.
  • Handle: RePEc:taf:japsta:v:38:y:2011:i:12:p:2939-2954
    DOI: 10.1080/02664763.2011.573542
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    References listed on IDEAS

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    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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    1. Fritsch, Markus & Haupt, Harry & Ng, Pin T., 2016. "Urban house price surfaces near a World Heritage Site: Modeling conditional price and spatial heterogeneity," Regional Science and Urban Economics, Elsevier, vol. 60(C), pages 260-275.
    2. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    3. Wattanawongwan, Suttisak & Mues, Christophe & Okhrati, Ramin & Choudhry, Taufiq & So, Mee Chi, 2023. "Modelling credit card exposure at default using vine copula quantile regression," European Journal of Operational Research, Elsevier, vol. 311(1), pages 387-399.
    4. Xu, Qifa & Niu, Xufeng & Jiang, Cuixia & Huang, Xue, 2015. "The Phillips curve in the US: A nonlinear quantile regression approach," Economic Modelling, Elsevier, vol. 49(C), pages 186-197.
    5. Kagerer, Kathrin, 2013. "A short introduction to splines in least squares regression analysis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 472, University of Regensburg, Department of Economics.

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