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http://dx.doi.org/10.5351/CSAM.2014.21.5.435

The Bandwidth from the Density Power Divergence

Pak, Ro Jin (Department of Applied Statistics, Dankook University)

Publication Information

Communications for Statistical Applications and Methods / v.21, no.5, 2014 , pp. 435-444 More about this Journal

Abstract

The most widely used optimal bandwidth is known to minimize the mean integrated squared error(MISE) of a kernel density estimator from a true density. In this article proposes, we propose a bandwidth which asymptotically minimizes the mean integrated density power divergence(MIDPD) between a true density and a corresponding kernel density estimator. An approximated form of the mean integrated density power divergence is derived and a bandwidth is obtained as a product of minimization based on the approximated form. The resulting bandwidth resembles the optimal bandwidth by Parzen (1962), but it reflects the nature of a model density more than the existing optimal bandwidths. We have one more choice of an optimal bandwidth with a firm theoretical background; in addition, an empirical study we show that the bandwidth from the mean integrated density power divergence can produce a density estimator fitting a sample better than the bandwidth from the mean integrated squared error.

Keywords

Density estimator; density power divergence; Kullback-Leibler divergence; $L_2$ distance; mean integrated square error;

Citations & Related Records

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