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The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics

✍ Scribed by Deli Li; M. Bhaskara Rao; R.J. Tomkins

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
183 KB
Volume
78
Category
Article
ISSN
0047-259X

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✦ Synopsis

The Chung Smirnov law of the iterated logarithm and the Finkelstein functional law of the iterated logarithm for empirical processes are used to establish new results on the central limit theorem, the law of the iterated logarithm, and the strong law of large numbers for L-statistics with certain bounded and smooth weight functions. These results are used to obtain necessary and sufficient conditions for almost sure convergence and for convergence in distribution of some wellknown L-statistics and U-statistics, including Gini's mean difference statistic. A law of the logarithm for weighted sums of order statistics is also presented.

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