Optimal bandwidth selection for a kernel density with a location-scale property

Aydın C., Gündüz N., Balibeyoğlu J.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.50, no.7, pp.1671-1684, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1080/03610926.2020.1804586
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1671-1684
  • Keywords: Kernel estimation, location-scale family, bias, density functional estimate, optimal bandwidth
  • Gazi University Affiliated: Yes

Abstract

This paper proposes a novel estimator of the bandwidth in kernel density estimation, built from an adaptive combination of the strengths of classical kernel smoothing and the desirable properties inherent in adjusted kernel smoothing as studied under a variety location and scale family of functions. The optimal bandwidth exists as a function of density functionals derived as the minimizer of the mean square error. We provide a substantial computational assessment of the performance of our proposed estimator on both simulated and real data, and it is very encouraging to notice that our proposed method exhibits a lower variance than its previous counterparts, and also yields an overall smaller mean squared error.