English

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

Keywords

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

R2 v1 2026-06-21T22:12:42.161Z