publication . Preprint . Article . 2016

On the rate of convergence in de Finetti’s representation theorem

Mijoule, Guillaume; Peccati, Giovanni; Swan, Yvik;
Open Access French
  • Published: 25 Jan 2016
Abstract
A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables $(X_k)_{k\geq1}$, there exists a probability measure $\mu$ on the Borel sets of $[0,1]$ such that $\bar X_n = n^{-1} \sum_{i=1}^n X_i$ converges weakly to $\mu$. For a wide class of probability measures $\mu$ having smooth density on $(0,1)$, we give bounds of order $1/n$ with explicit constants for the Wasserstein distance between the law of $\bar X_n$ and $\mu$. This extends a recent result {by} Goldstein and Reinert \cite{goldstein2013stein} regarding the distance between the scaled number of white balls drawn in a P\'olya-Eggenberger ...
Subjects
free text keywords: Probabilités, Mathematics - Probability, Statistique mathématique
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publication . Preprint . Article . 2016

On the rate of convergence in de Finetti’s representation theorem

Mijoule, Guillaume; Peccati, Giovanni; Swan, Yvik;