A strong law of large numbers for U-statistics
Date
1992Source
Journal of Statistical Planning and InferenceVolume
31Issue
2Pages
133-145Google Scholar check
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A U-statistic is defined based on a symmetric kernel h and on a collection of r-dimensionally indexed independent random variables from a distribution F. The simplest case of such a U-statistic is the sample mean of an array of multidimensionally indexed random variables. In this paper, we present the strong law of large numbers for this class of U-statistics under the moment condition EF{|h| (log+ |h|)r-1} < ∞, thus generalizing the strong law of large numbers of Smythe (1973) and Etemadi (1981). © 1992.