An isometric study of the Lindeberg-Feller CLT via Stein's method

2011/12/24 by Ben Berckmoes, Berckmoes, Ben, Bob Lowen +3
Physics and Astronomy · #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.1112.5719

Abstract

We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.

Related

• Approximate central limit theorems
• Kolmogorov bounds for decomposable random variables and subgraph counting by the Stein-Tikhomirov method
• Stein's method for max-stable random vectors
• Stein's method for normal approximation in Wasserstein distances with\n application to the multivariate Central Limit Theorem
• Dickman Approximation of weighted random sums in the Kolmogorov distance