Consistance d'un estimateur de minimum de variance étendue

Details Consistance d'un estimateur de minimum de variance étendue Consistance d'un estimateur de minimum de variance étendue

2008-02-21

arxiv.org/abs/0802.3190v1

Comptes Rendus de l Acad\'emie des Sciences - Series I - Mathematics 341 (2005) 133-136

Mathematics

Statistics Theory

Scientific paper

We consider a generalization of the criterion minimized by the K-means algorithm, where a neighborhood structure is used in the calculus of the variance. Such tool is used, for example with Kohonen maps, to measure the quality of the quantification preserving the neighborhood relationships. If we assume that the parameter vector is in a compact Euclidean space and all it components are separated by a minimal distance, we show the strong consistency of the set of parameters almost realizing the minimum of the empirical extended variance.

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