The Region of Positivity and Unimodality in the Truncated Series of a Nonparametric Kernel Density Estimator

  • Gupta, A.K. (Department of Mathematics and Statistics, Bowling Green State University) ;
  • Im, B.K.K. (Department of Mathematics and Statistics, Memorial University of Newfoundland, Canada)
  • 발행 : 1981.12.01

초록

This paper approximates to a kernel density estimate by a truncated series of expansion involving Hermite polynomials, since this could ease the computing burden involved in the kernel-based density estimation. However, this truncated series may give a multimodal estimate when we are estiamting unimodal density. In this paper we will show a way to insure the truncated series to be positive and unimodal so that the approximation to a kernel density estimator would be maeningful.

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