Recently, using data on Canadian housing, Parmeter, Henderson, and Kumbhakar (2007) found that a nonparametric approach for estimating hedonic prices is superior to formerly suggested parametric and semiparametric specifications. We carefully analyze this data set by applying a nonparametric specification test and simulation based forecast comparisons. For the case at issue our results suggest that a previously proposed parametric specification cannot be rejected.
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.
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