Modal regression models based on B-splines

A nonparametric model based on B-splines is given for modal regression. The existing nonparametric local polynomial modal regression performs well in goodness of fit but with high computational complexity. Given the nice properties of B-splines, modal regression based on B-splines contains the same performance for estimation compared to that of local polynomial modal regression but requires much less computational burden. We also establish asymptotic properties for the proposed estimator under noise density assumptions. As the commonly used cross-validation hyperparameter selection criteria are not suitable for modal regression, we construct a new cross-validation hyperparameter selection criterion. Furthermore, simulations and applications show that this criterion behaves well for modal regression.