Consistency of the $α$-trimming of a probability. Applications to central regions
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The sequence of $α$-trimmings of empirical probabilities is shown to converge, in the Painlevé--Kuratowski sense, on the class of probability measures endowed with the weak topology, to the $α$-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.
Published in at http://dx.doi.org/10.3150/07-BEJ109 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
Published in at http://dx.doi.org/10.3150/07-BEJ109 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)