On the error bound in the normal approximation for Jack measures
Tác giả: Louis Chen, Martin Raic, Lê Văn Thành
Bernoulli
Quyển: Trang:
Năm xuất bản: 1/2021
Tóm tắt
In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein’s method and zero-bias couplings. Our uniform bound comes very close to that conjectured by Fulman (J. Combin. Theory Ser. A 108 (2004) 275–296). As a by-product of the proof of the non-uniform bound, we obtain a Rosenthal-type inequality for zero-bias couplings.
Từ khóa
Jack deformation, Jack measure, Kolmogorov distance, non-uniform bound, rate of convergence, Stein’s method, uniform bound, zero-bias coupling
