Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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The Bandwidth from the Density Power Divergence

  • Pak, Ro Jin (Department of Applied Statistics, Dankook University)
  • Received : 2014.07.08
  • Accepted : 2014.08.17
  • Published : 2014.09.30
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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.

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References

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