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Asymptotics of a clustering criterion for smooth distributions. (English) Zbl 1336.62172
Summary: 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.

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62E20 Asymptotic distribution theory in statistics
62F05 Asymptotic properties of parametric tests
62G30 Order statistics; empirical distribution functions
60F17 Functional limit theorems; invariance principles
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