A Nonuniform Bound to an Independent Test in High Dimensional Data Analysis via Stein's Method. (3rd February 2019)

• Record Type: Journal Article
• Authors: Rerkruthairat, Nahathai
• Other Names: De Gregorio Alessandro Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2019(2019)
• Publication Date: 2019-02-03
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2019/8641870
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : The Berry-Esseen bound for the random variable based on the sum of squared sample correlation coefficients and used to test the complete independence in high diemensions is shown by Stein's method. Although the Berry-Esseen bound can be applied to all real numbers inR, a nonuniform bound at a real numberz usually provides a sharper bound ifz is fixed. In this paper, we present the first version of a nonuniform bound on a normal approximation for this random variable with an optimal rate of1 / 0.5 + | z | · O 1 / m by using Stein's method.