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