## The Annals of Statistics

### Trimmed $k$-means: an attempt to robustify quantizers

#### Abstract

A class of procedures based on "impartial trimming" (self-determined by the data) is introduced with the aim of robustifying k-means, hence the associated clustering analysis. We include a detailed study of optimal regions, showing that only nonpathological regions can arise from impartial trimming procedures. The asymptotic results provided in the paper focus on strong consistency of the suggested methods under widely general conditions. A section is devoted to exploring the performance of the procedure to detect anomalous data in simulated data sets.

#### Article information

Source
Ann. Statist. Volume 25, Number 2 (1997), 553-576.

Dates
First available in Project Euclid: 12 September 2002

http://projecteuclid.org/euclid.aos/1031833664

Digital Object Identifier
doi:10.1214/aos/1031833664

Mathematical Reviews number (MathSciNet)
MR1439314

Zentralblatt MATH identifier
0878.62045

#### Citation

Cuesta-Albertos, J. A.; Gordaliza, A.; Matrán, C. Trimmed $k$-means: an attempt to robustify quantizers. Ann. Statist. 25 (1997), no. 2, 553--576. doi:10.1214/aos/1031833664. http://projecteuclid.org/euclid.aos/1031833664.

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