publication . Other literature type . Article . 1986

On Improving Density Estimators which are not Bona Fide Functions

Leslaw Gajek;
Open Access English
  • Published: 01 Dec 1986
  • Publisher: The Institute of Mathematical Statistics
In order to improve the rate of decrease of the IMSE for nonparametric kernel density estimators with nonrandom bandwidth beyond $O(n^{-4/5})$ all current methods must relax the constraint that the density estimate be a bona fide function, that is, be nonnegative and integrate to one. In this paper we show how to achieve similar improvement without relaxing any of these constraints. The method can also be applied for orthogonal series, adaptive orthogonal series, spline, jackknife, and other density estimators, and assures an improvement of the IMSE for each sample size.
free text keywords: Nonparametric density estimation, kernel estimation, orthogonal series estimation, rates of convergence, 62G05, Statistics, Probability and Uncertainty, Statistics and Probability
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