A Note on Density Estimation Using Orthogonal Expansions

Abstract

The estimation of probability density functions is frequently approached through the use of orthogonal series. The goodness of the estimator can be conveniently measured in terms of Mean Integrated Squared Error, or MISE. To reduce MISE to a minimum, for fixed sample size, the experimenter would like to determine an optimal truncation point for the orthogonal series estimator. Presented here are some general MISE properties of a commonly used type of density estimator.