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.

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...

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...

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 )...

In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeometric 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 Hypergeometric and t...

University of Southern California and University of Melbourne We introduce a new family of distributions to approximate P(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 s...