Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

Kai Krokowski; Anselm Reichenbachs; Christoph Thaele

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arXiv · 1404.0962

Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

Kai Krokowski·Anselm Reichenbachs·Christoph Thaele

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Abstract

Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a connection to small-ball probabilities and shed new light onto the relation between central limit theorems on the Rademacher chaos and norms of contraction operators. Applications concern infinite weighted 2-runs, a combinatorial central limit theorem and traces of Bernoulli random matrices.

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BibTeX RIS

Kai Krokowski, Anselm Reichenbachs, Christoph Thaele. 2014-04-03. Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences. https://arxiv.org/abs/1404.0962

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