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July, 1978 Estimation of a Multivariate Mode
Thomas W. Sager
Ann. Statist. 6(4): 802-812 (July, 1978). DOI: 10.1214/aos/1176344253


Consider a random sample from an absolutely continuous multivariate distribution. Let $\mathscr{J}$ be a class of sets which are not too long and thin. A point $\mathbf{\theta}_n$ chosen from a minimum volume set $S_n \in \mathscr{J}$ containing at least $r = r(n)$ of the data may be used as an estimate of the mode of the distribution. In this paper, it is shown that $\mathbf{\theta}_n$ converges almost surely to the true mode under very minor conditions on $\{r(n)\}$ and the distribution. Convergence rates are also obtained. Extensions to estimation of local and/or multiple modes are noted. Finally, computational simplifications resulting from choosing $S_n$ from spheres or cubes centered at observations are discussed.


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Thomas W. Sager. "Estimation of a Multivariate Mode." Ann. Statist. 6 (4) 802 - 812, July, 1978.


Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62037
MathSciNet: MR491553
Digital Object Identifier: 10.1214/aos/1176344253

Primary: 62G05
Secondary: 60F15 , 62H99

Keywords: consistency , Convergence rates , estimation , Mode , multivariate

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 4 • July, 1978
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