Boundary performance of the beta kernel estimators

Shunpu Zhang, Rohana J. Karunamuni

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The beta kernel estimators are shown in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131-145] to be non-negative and have less severe boundary problems than the conventional kernel estimator. Numerical results in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131-145] further show that beta kernel estimators have better finite sample performance than some of the widely used boundary corrected estimators. However, our study finds that the numerical comparisons of Chen are confounded with the choice of the bandwidths and the quantities being compared. In this paper, we show that the performances of the beta kernel estimators are very similar to that of the reflection estimator, which does not have the boundary problem only for densities exhibiting a shoulder at the endpoints of the support. For densities not exhibiting a shoulder, we show that the beta kernel estimators have a serious boundary problem and their performances at the boundary are inferior to that of the well-known boundary kernel estimator.

Original languageEnglish (US)
Pages (from-to)81-104
Number of pages24
JournalJournal of Nonparametric Statistics
Volume22
Issue number1
DOIs
StatePublished - Jan 2010

Keywords

  • Beta kernel estimator
  • Boundary kernel estimator
  • Boundary problem
  • Nonparametric density estimation
  • Reflection estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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