کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1149472 957880 2011 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Asymptotically optimal Berry–Esseen-type bounds for distributions with an absolutely continuous part
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Asymptotically optimal Berry–Esseen-type bounds for distributions with an absolutely continuous part
چکیده انگلیسی

Recursive and closed form upper bounds are offered for the Kolmogorov and the total variation distance between the standard normal distribution and the distribution of a standardized sum of n independent and identically distributed random variables. The method employed is a modification of the method of compositions along with Zolotarev's ideal metric. The approximation error in the CLT obtained vanishes at a rate O(n−k/2+1), provided that the common distribution of the summands possesses an absolutely continuous part, and shares the same k  −1 (k⩾3)(k⩾3) first moments with the standard normal distribution. Moreover, for the first time, these new uniform Berry–Esseen-type bounds are asymptotically optimal, that is, the ratio of the true distance to the respective bound converges to unity for a large class of distributions of the summands. Thus, apart from the correct rate, the proposed error estimates incorporate an optimal asymptotic constant (factor). Finally, three illustrative examples are presented along with numerical comparisons revealing that the new bounds are sharp enough even to be used in practical statistical applications.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 141, Issue 3, March 2011, Pages 1250–1268
نویسندگان
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