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

Grzegorz Rempala

Statistics & Probability Letters, 1998, vol. 39, issue 3, 263-270

Abstract: Let Unm 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 --> [infinity]. In this work we are concerned with establishing the strong consistency properties for Unm 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 Unm.

Keywords: U-statistics; of; varying; order; Martingale; difference; decomposition; Complete; convergence; Strong; law; of; large; numbers; for; the; arrays; of; random; variables (search for similar items in EconPapers)
Date: 1998
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