ONE-SIDED REFINEMENTS OF THE STRONG LAW OF LARGE NUMBERS AND THE GLIVENK-CANTELLI THEOREM
成果类型：
Article
署名作者：
GILAT, D; HILL, TP
署名单位：
University System of Georgia; Georgia Institute of Technology
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989688
发表日期：
1992
页码：
1213-1221
关键词：
摘要：
A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refinement of the Glivenko-Cantelli theorem is obtained, in which a new empirical distribution function not only has the usual uniformly almost-sure convergence property of the classical empirical distribution function, but also has the property that all its quantiles converge almost surely. A tool in the proofs is a strong law of large numbers for order statistics.
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