Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples

El-Dakkak, Omar; Peccati, Giovanni; Prünster, Igor

doi:10.1016/j.jmva.2014.04.012

Cited by 3 publications

(2 citation statements)

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“…To the best of our knowledge, the closest result to ours is due to [10] and concerns the classical Pólya-Eggenberger urn model (see e.g. [18] for a general discussion, as well as [7,8,17] for several recent developments). This model is constructed as follows : at time 0, an urn contains A ≥ 1 white balls and B ≥ 1 black balls and at every positive integer time, a ball is randomly drawn from the urn (independently of the past) and replaced along with m ≥ 1 additional balls of the same color.…”

Section: Overview and Frameworkmentioning

confidence: 89%

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

Mijoule¹,

Peccati²,

Swan³

2016

ALEA

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A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables (X k ) k≥1 , there exists a probability measure µ on the Borel sets of [0, 1] such thatX n = n −1 n i=1 X i converges weakly to µ. For a wide class of probability measures µ having smooth density on (0, 1), we give bounds of order 1/n with explicit constants for the Wasserstein distance between the law ofX n and µ. This extends a recent result by Goldstein and Reinert [10] regarding the distance between the scaled number of white balls drawn in a Pólya-Eggenberger urn and its limiting distribution. We prove also that, in the most general cases, the distance between the law ofX n and µ is bounded below by 1/n and above by 1/ √ n (up to some multiplicative constants). For every δ ∈ [1/2, 1], we give an example of an exchangeable sequence such that this distance is of order 1/n δ .

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Section: Overview and Frameworkmentioning

confidence: 89%

“…Exchangeable sequences such that the associated de Finetti measure has support contained in (0, 1) are sometimes called non-deterministic -see e.g. [7,8,14,17].…”

Section: Preliminariesmentioning

confidence: 99%