Consistency of the $α$-trimming of a probability. Applications to central regions

Details Consistency of the $α$-trimming of a probability. Applications to central regions Consistency of the $α$-trimming of a probability. Applications to central regions

2008-05-15

arxiv.org/abs/0805.2219v1

Bernoulli 2008, Vol. 14, No. 2, 580-592

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ109 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/07-BEJ109

The sequence of $\alpha$-trimmings of empirical probabilities is shown to
converge, in the Painlev\'{e}--Kuratowski sense, on the class of probability
measures endowed with the weak topology, to the $\alpha$-trimming of the
population probability. Such a result is applied to the study of the asymptotic
behaviour of central regions based on the trimming of a probability.

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