An isometric study of the Lindeberg-Feller central limit theorem via Stein's method

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Berckmoes, B.¹  Lowen, R.¹  Van Casteren, J.¹ 

[1] Univ Antwerp, Dept Math & Comp Sci, Antwerp, Belgium

关键词: Approach structure;    Distance;    Limit;    Weak topology;    Probability measure;    Law;    Random variable;    Central limit theorem;    Lindeberg condition;    Kolmogorov metric;    Triangular array;   

DOI  :  10.1016/j.jmaa.2013.04.012

来源: Elsevier

【 摘 要 】

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. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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