Ratios Running head: Berry-Esseen Theorem for Character Ratios Submitted 3/9/05; Revised 8/6/06 By Jason Fulman Department of Mathematics, University of Southern California Los Angeles, CA 90089, USA [email protected] Abstract: Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We m...

Bolthausen used a variation of Stein's method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.

By Jason Fulman Department of Mathematics, University of Southern California Los Angeles, CA 90089, USA [email protected] Abstract: Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representa...

length-biased data are widely seen in applications. they are mostly applicable in epidemiological studies or survival analysis in medical researches. here we aim to propose a berry-esseen type bound for the kernel density estimator of this kind of data.the rate of normal convergence in the proposed berry-esseen type theorem is shown to be o(n^(-1/6) ) modulo logarithmic term as n tends to infin...

Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...

In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeomet-ric distribution for weak convergence to a Normal limit. We establish a Berry-Esseen theorem for the Hypergeometric distribution solely under this necessary and sufficient condition. We further derive a nonuniform Berry-Esseen bound where the tails of the difference between the Hypergeo-metric and...

We introduce a new family of distributions to approximate IP(W ∈ A) for A ⊂ {· · · ,−2,−1, 0, 1, 2, · · · } and W a sum of independent integer-valued random variables ξ1, ξ2, · · · , ξn with finite second moments, where with large probability W is not concentrated on a lattice of span greater than 1. The well-known Berry–Esseen theorem states that for Z a normal random variable with mean IE(W )...

We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and the Cauchy transform of the limiting operator-valued semicircular element.

In this paper, we generalize the asymptotic result of Esseen (1958) concerning the Wasserstein distance of order one in the mean central limit theorem to the Wasserstein distances of order r for r in ]1, 2].