Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples
Probability
2012-05-24 v1 Statistics Theory
Statistics Theory
Abstract
We study Hoeffding decomposable exchangeable sequences with values in a finite set D. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, if the cardinality of D is strictly greater than 2, then there exists a class of neither P\'{o}lya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable. The construction of such sequences is based on some ideas appearing in Hill, Lane and Sudderth [1987] and answers a question left open in El-Dakkak and Peccati [2008].
Cite
@article{arxiv.1205.5138,
title = {Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples},
author = {Omar El-Dakkak and Giovanni Peccati and Igor Prünster},
journal= {arXiv preprint arXiv:1205.5138},
year = {2012}
}