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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


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.


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Thomas W. Sager. "Consistency in Nonparametric Estimation of the Mode." Ann. Statist. 3 (3) 698 - 706, May, 1975.


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

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

Primary: 62G05
Secondary: 60F15

Keywords: consistency , Convergence rates , estimation , Mode

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 3 • May, 1975
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