Electronic Journal of Statistics

Asymptotics of a clustering criterion for smooth distributions

Karthik Bharath, Vladimir Pozdnyakov, and Dipak K. Dey

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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.

Article information

Electron. J. Statist., Volume 7 (2013), 1078-1093.

First available in Project Euclid: 15 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F05: Asymptotic properties of tests 62G30: Order statistics; empirical distribution functions
Secondary: 60F17: Functional limit theorems; invariance principles 62M02: Markov processes: hypothesis testing

Clustering trimmed means CLT


Bharath, Karthik; Pozdnyakov, Vladimir; Dey, Dipak K. Asymptotics of a clustering criterion for smooth distributions. Electron. J. Statist. 7 (2013), 1078--1093. doi:10.1214/13-EJS801. https://projecteuclid.org/euclid.ejs/1366031051

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