A new bandwidth selection method for nonparametric modal regression based on generalized hyperbolic distributions

Abstract

As a complement to standard mean and quantile regression, nonparametric modal regression has been broadly applied in various fields. By focusing on the most likely conditional value of Y given x, the nonparametric modal regression is shown to be resistant to outliers and some forms of measurement error, and the prediction intervals are shorter when data is skewed. However, the bandwidth selection is critical but very challenging, since the traditional least-squares based cross-validation method cannot be applied. We propose to select the bandwidth by applying the asymptotic global optimal bandwidth and the flexible generalized hyperbolic (GH) distribution as the distribution of the error. Unlike the plug-in method, the new method does not require preliminary parameters to be chosen in advance, is easy to compute by any statistical software, and is computationally efficient compared to the existing kernel density estimator (KDE) based method. Numerical studies show that the GH based bandwidth performs better than existing bandwidth selector, in terms of higher coverage probabilities. Real data applications also illustrate the superior performance of the new bandwidth.