SOME PROPERTIES OF METRICS IN A STUDY ON CONVERGENCE TO NORMALITY

被引：31

作者：

HEYDE, CC

机构：

[1] Department of Statistics, Australian Natural University, School of General Studies, Canberra, 2600, A. C. T., Box 4, P. O.

来源：

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE | 1969年 / 11卷 / 03期

关键词：

D O I：

10.1007/BF00536379

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper is concerned with the use of the ℒ1 and ℒ∞ metrics in a study of certain properties and implications of convergence rates in the central limit theorem for sums of independent and identically distributed random variables which belong to the domain of attraction of the normal distribution. Also, some general convergence rate results on the ℒ∞ metric obtained under the assumption of a finite second moment are used as a vital tool in a new proof of the classical iterated logarithm law and in extending the scope of classical methods for the proof of other similar results of a more general kind. © 1969 Springer-Verlag.

引用

页码：181 / &

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