An Inductive Proof of the Berry-Esseen Theorem for Character Ratios Running head: Berry-Esseen Theorem for Character Ratios Submitted 3/9/05; Revised 8/6/06
نویسنده
چکیده
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 representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.
منابع مشابه
An Inductive Proof of the Berry-Esseen Theorem for Character Ratios Running head: Berry-Esseen Theorem for Character Ratios
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...
متن کاملAn Inductive Proof of the Berry-Esseen Theorem for Character Ratios
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.
متن کاملA Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
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...
متن کاملar X iv : m at h / 06 02 27 6 v 1 [ m at h . PR ] 1 3 Fe b 20 06 A Sub - Gaussian Berry - Esseen Theorem For the Hypergeometric Distribution
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...
متن کاملThe Berry-esseen Bound for Character Ratios
Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let χλ(12) be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let dim(λ) be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate of O(n−s) for any 0 < s < 1 2 in the central limit theorem...
متن کامل