Strong law of large numbers for weighted U-statistics: Application to incomplete U-statistics

Masoud M. Nasari

Statistics & Probability Letters, 2012, vol. 82, issue 6, 1208-1217

Abstract: In this exposition we investigate almost sure convergence for weighted U-statistics. This strong law of large numbers is established for a class of divergent series of non-negative weights when the product of the kernel of the underlying weighted U-statistics and its logarithm is integrable. This result is used to establish the almost sure validity of incomplete U-statistics. Also, a method of constructing incomplete U-statistics of order 2 is introduced and its almost sure validity is established.

Keywords: Strong law of large numbers; Weighted U-statistics; Incomplete U-statistics; Reduction scheme (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2012.03.010

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