BOUNDS ON THE CONSTANT IN THE MEAN CENTRAL LIMIT THEOREM BY LARRY GOLDSTEIN University of Southern California
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چکیده
Let X 1 ,. .. , X n be independent with zero means, finite variances σ 2 1 ,. .. , σ 2 n and finite absolute third moments. Let F n be the distribution function of (X 1 + · · · + X n)/σ , where σ 2 = n i=1 σ 2 i , and that of the standard normal. The L 1-distance between F n and then satisfies
منابع مشابه
2 1 N ov 2 00 5 Berry Esseen Bounds for Combinatorial Central Limit Theorems and Pattern Occurrences , using Zero and Size Biasing ∗ † Larry Goldstein University of Southern California
Berry Esseen type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random permutation has either the uniform distribution or one which is constant over permutations with the same cycle type and having no fixed points. The size biasing bounds ...
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تاریخ انتشار 2010