A local cross-validation algorithm

Abstract

The usuall form of cross-validation is global in character, and is designed to estimate a density in some "average" sense over its entire support. In this paper we present a local version of squared-error cross-validation, suitable for estimating a probability density at a given point. It is shown theoretically to be asymptotically optimal in the sense of minimizing mean squared error. Numerical examples illustrate finite sample characteristic, and show that local cross-validation is a practical algorithm.cross-validation density estimation kernel method local estimation window size