Open Access
Translator Disclaimer
May, 1975 Consistency in Nonparametric Estimation of the Mode
Thomas W. Sager
Ann. Statist. 3(3): 698-706 (May, 1975). DOI: 10.1214/aos/1176343132

Abstract

Let $X$ be an absolutely continuous real-valued random variable with additional restrictions to be imposed later. Venter (1967) ("On estimation of the mode," Ann. Math. Statist. 37 1446-1455) estimated the mode of $X$ by a point from the shortest interval containing a specified number $r = r(n)$ of observations. Venter demonstrated that such an estimator is strongly consistent under appropriate conditions on the distribution of $X$ and on $r(n)$. It is the purpose of this paper to show that strong consistency actually holds under very general conditions on the distribution of $X$. Convergence rates are also obtained which are, in some cases, much faster than those reported by Venter.

Citation

Download Citation

Thomas W. Sager. "Consistency in Nonparametric Estimation of the Mode." Ann. Statist. 3 (3) 698 - 706, May, 1975. https://doi.org/10.1214/aos/1176343132

Information

Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0303.62037
MathSciNet: MR373142
Digital Object Identifier: 10.1214/aos/1176343132

Subjects:
Primary: 62G05
Secondary: 60F15

Keywords: consistency , Convergence rates , estimation , Mode

Rights: Copyright © 1975 Institute of Mathematical Statistics

JOURNAL ARTICLE
9 PAGES


SHARE
Vol.3 • No. 3 • May, 1975
Back to Top