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Strong law of large numbers for U-statistics of varying order

✍ Scribed by Grzegorz Rempała

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
322 KB
Volume
39
Category
Article
ISSN
0167-7152

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✦ Synopsis

Let U m be a U-statistic of order m based on n i.i.d, real random variables. Suppose that m = m(n) changes with n as n--+ cx~. In this work we are concerned with establishing the strong consistency properties for U~ under linear norming. The results are obtained by generalizing the SLLN for arrays of rowwise independent random variables (Hu et al., 1989) to the case of rowwise martingale differences and applying standard martingale decompositions of U,, ~.

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