Sequential Bayesian bandwidth selection for multivariate kernel regression with applications

Abstract

A new Bayesian bandwidth selection procedure is proposed for nonparametric kernel estimates based on the sequential Monte Carlo method. Compared with the existing Bayesian bandwidth selector of Zhang et al. (2009), this new method can enhance the convergence to the global optimum with a substantially faster computation speed. In particular, the method offers an improved out-of-sample performance as shown by simulations. The bandwidth selector is applied to the option state price density, production function, and nonparametric relationship between oil and stock index returns; results indicate that our proposed method outperforms other methods in terms of the mean square error and log-likelihood in all applications.