Cross-validating fit and predictive accuracy of nonlinear quantile regressions

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 kernelbased 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.

The Phillips curve in the US: A nonlinear quantile regression approach

“…To evaluate the performance of the chosen linear and nonlinear QRPC models (the order l and k are selected), following the suggestion of Haupt et al (2011), we provide a model comparison procedure by examining the estimation accuracy and prediction ability of different models.…”

Modelling and Optimisation of Resource Usage in an IoT Enabled Smart Campus

“…RMSE is most useful when large errors are particularly undesirable since errors are squared, giving a relatively higher weight to larger errors, before being averaged. Additionally, we employ the average weighted absolute error (WMAE) [184] to evaluate the performance of prediction when under-prediction is considered more costly than over-prediction.…”