A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator

Abstract

The estimation of multivariate densities using the kernel method has wide applicability. However, this problem has received less attention than the univariate case. This is mainly due to the increasing difficulty in estimating the optimal smoothing matrix, especially when the components are correlated. To overcome this difficulty, we propose in this work a Bayesian method to estimate the optimal smoothing matrix H. A loss function is defined and the estimator of H is the matrix minimising the loss function. We carried out simulations with a mixture of multivariate densities with correlation and the results were highly satisfactory.