Data-driven choice of the smoothing parametrization for kernel density estimators

Abstract

There are several levels of sophistication when specifying the bandwidth matrix $\mathbf{H}$ to be used in a multivariate kernel density estimator, including $\mathbf{H}$ to be a positive multiple of the identity matrix, a diagonal matrix with positive elements or, in its most general form, a symmetric positive-definite matrix. In this paper, the author proposes a data-based method for choosing the smoothing parametrization to be used in the kernel density estimator. The procedure is fully illustrated by it simulation study and some real data examples.