An Anscombe-type theorem
Probability
2012-10-01 v1 Statistics Theory
Statistics Theory
Abstract
Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well. Key words and phrases: Anscombe theorem, Exchangeability, Random indices, Random sums, Stable convergence
Cite
@article{arxiv.1209.6473,
title = {An Anscombe-type theorem},
author = {Patrizia Berti and Irene Crimaldi and Luca Pratelli and Pietro Rigo},
journal= {arXiv preprint arXiv:1209.6473},
year = {2012}
}
Comments
10 pages, preprint