CASE WESTERN RESERVE UNIVERSITY

STATISTICS COLLOQUIUM

Abstract

Theoretical and practical aspects of the sample-point locally adaptive density estimator are examined. Through binning a closed form expression for the mean integrated squared error (MISE) can be obtained. With such an expression, the behavior of an optimally adaptive smoothing parameter function is studied for the first time. This approach differs from earlier techniques in that the bias remains O(h2) and is not ilimprovedli to the higher-order rate of O(h4). In addition, a practical algorithm is constructed using a modification of least-squares cross validation. Several examples will be shown to demonstrate the method and comparisons made to a fixed bandwidth estimator and a fully automatic version of Abramson's square-root law (Abramson, 1982). Extensions to higher dimensions will also be explored.