## 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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### References:

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