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June 1999 A central limit theorem for multivariate generalized trimmed $k$-means
Luis A. García-Escudero, Alfonso Gordaliza, Carlos Matrán
Ann. Statist. 27(3): 1061-1079 (June 1999). DOI: 10.1214/aos/1018031268

Abstract

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.

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Luis A. García-Escudero. Alfonso Gordaliza. Carlos Matrán. "A central limit theorem for multivariate generalized trimmed $k$-means." Ann. Statist. 27 (3) 1061 - 1079, June 1999. https://doi.org/10.1214/aos/1018031268

Information

Published: June 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0984.62042
MathSciNet: MR1724041
Digital Object Identifier: 10.1214/aos/1018031268

Subjects:
Primary: 60F05 , 62H20
Secondary: 62G15 , 62G35

Keywords: central limit theorem , clustering , impartial trimming , K-means , robustness , tolerance zones

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 3 • June 1999
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