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2013 Asymptotics of a clustering criterion for smooth distributions
Karthik Bharath, Vladimir Pozdnyakov, Dipak K. Dey
Electron. J. Statist. 7: 1078-1093 (2013). DOI: 10.1214/13-EJS801

Abstract

We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed. The asymptotic behavior of the point at which the observations are split into two clusters is examined. The results obtained can then be utilized to construct an interval estimate of the point which splits the data and develop tests for bimodality and presence of clusters.

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Karthik Bharath. Vladimir Pozdnyakov. Dipak K. Dey. "Asymptotics of a clustering criterion for smooth distributions." Electron. J. Statist. 7 1078 - 1093, 2013. https://doi.org/10.1214/13-EJS801

Information

Published: 2013
First available in Project Euclid: 15 April 2013

zbMATH: 1336.62172
MathSciNet: MR3044510
Digital Object Identifier: 10.1214/13-EJS801

Subjects:
Primary: 62F05, 62G30
Secondary: 60F17, 62M02

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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