page loader
  1. Home
  2. Bài báo khoa học
  3. Chi tiết bài báo
On the error bound in the normal approximation for Jack measures
Authors: Louis Chen, Martin Raic, Lê Văn Thành
404    0
Bernoulli
:     :
: https://projecteuclid.org/journals/bernoulli/volume-27/issue-1/On-the-error-bound-in-the-normal-approximation-for-Jack/10.3150/20-BEJ1245.short
: 1523-2021-bernoulli-on-the-error-bound-in-the-normal-approximation.pdf
Publishing year: 1/2021
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.
Jack deformation, Jack measure, Kolmogorov distance, non-uniform bound, rate of convergence, Stein’s method, uniform bound, zero-bias coupling
On the Laws of Large Numbers for Double Arrays of Independent Random Elements in Banach SpacesWeighted sums of strongly mixing random variables with an application to nonparametric regressionOn the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spacesOn complete convergence in mean for double sums of independent random elements in Banach spacesHien, Nguyen Thi Thanh; Thanh, Le Van; Van, Vo Thi Hong. On the negative dependence in Hilbert spaces with applications. Appl. Math. 64 (2019), no. 1, 45--59.Le Van Thanh and Nguyen Thi Thuy, Necessary and sufficient conditions for complete convergence of double weighted sums of pairwise independent identically distributed random elements in Banach spaces, Acta Mathematica Hungarica, Volume 157 (2019), Issue 2, 312–326 (SCIE).Lê Vǎn Thành and Nguyen Ngoc Tu, Error bounds in normal approximation for the squared-length of total spin in the mean field classical N-vector models, Electronic Communications in Probability, Volume 24 (2019) no. 16, 12 pp (SCIE).Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with ApplicationsOn the Baum-Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constantsOn an extension of the Borel--Cantelli lemma for double arrays of dependent random variablesThe Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing SequencesOn convergence in mean for double arrays of pairwise independent random variablesA note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbersThe Hsu-Robbins-Erdös theorem for the maximum partial sums of quadruplewise independent random variablesOn the (p,q)-type strong law of large numbers for sequences of independent random variablesOn a new concept of stochastic domination and the laws of large numbersOn weak laws of large numbers for maximal partial sums of pairwise independent random variablesOptimal bounds in normal approximation for many interacting worldsOptimal moment conditions for complete convergence for maximal normed weighted sums from arrays of rowwise independent random elements in Banach spacesMean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chainsAlmost sure summability of the maximal normed partial sums of m-dependent random elements in Banach spacesSharp sufficient conditions for mean convergence of the maximal partial sums of dependent random variables with general norming sequencesOn Rio's proof of limit theorems for dependent random fieldsComplete convergence for the maximal partial sums without maximal inequalitiesMaximal inequalities for normed double sums of random elements in martingale type p Banach spaces with applications to degenerate mean convergence of the maximum of normed sumsSome Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random ElementsLaws of large numbers for pairwise independent random variablesProbability and Statistics