Kai Krokowski, Anselm Reichenbachs, Christoph Thaele
Published 2014-04-03, updated 2014-10-01Version 2
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.
On the error bound in a combinatorial central limit theorem
Berry-Esseen bounds for random projections of $\ell_p^n$-balls
Berry-Esseen bounds for functionals of independent random variables
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