Asymptotics of a Clustering Criterion for Smooth Distributions

Karthik Bharath; Vladimir Pozdnyakov; Dipak K Dey

doi:10.1214/13-ejs801

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arXiv · 1205.2123

Asymptotics of a Clustering Criterion for Smooth Distributions

Karthik Bharath·Vladimir Pozdnyakov·Dipak K Dey

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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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BibTeX RIS

Karthik Bharath, Vladimir Pozdnyakov, Dipak K Dey. 2013-04-01. Asymptotics of a Clustering Criterion for Smooth Distributions. https://doi.org/10.1214/13-ejs801

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