The application of “concentration” steps is the main principle behind Forgy’s k-means algorithm and the fast-MCD algorithm. Despite this coincidence, it is not completely straightforward to combine both algorithms for developing a clustering method which is not severely affected by few...

The equivalence of sequences of probability measures jointly with the extension of Skorohod's representation theorem due to Blackwell and Dubins is used to obtain strong convergence of weighted sums of random elements in a separable Banach space. Our results include most of the known work on...

The work is devoted to analyzing, from the asymptotic point of view, some examples of sequences of pairwise independent identically distributed random variables. Special attention is paid to the case of stationary sequences by the consideration of different situations that can arise in...

We first give some Glivenko-Cantelli-type theorems for the bootstrap. We prove almost sure convergence and convergence in probability. The results involve conditions on the resampling size which are not far from being (and often are) optimal. We next analyze the weak law of large numbers for the...