On the convergence of scaled random samples
成果类型：
Article
署名作者：
Pritchard, G
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1065725190
发表日期：
1996
页码：
1490-1506
关键词：
摘要：
The scaled-sample problem asks the following question: given a distribution on a normed linear space E, when do there exist constants {gamma(n)} such that {X((j))/gamma(n)}(n)(j=1) converges as n --> infinity (in the Hausdorff metric given by the norm) to a fixed set K? (Here {X((j))} i.i.d. with the given distribution.) The main result presented here relates the convergence of scaled samples to a large deviation principle for single observations, thereby achieving a dimension-free description of the problem.