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A central limit theorem for multivariate generalized trimmed \(k\)-means. (English) Zbl 0984.62042

Summary: A central limit theorem for generalized trimmed \(k\)-means is obtained in a very general framework that covers the multivariate setting, general penalty functions and general \(k\geq 1\). Several applications, including the location estimator case \((k=1)\) for elliptical distributions and the construction of multivariate (not necessarily connected) tolerance zones, are also given.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
60F05 Central limit and other weak theorems
62G35 Nonparametric robustness
62G15 Nonparametric tolerance and confidence regions
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