U-statistics on associated random variables
Date
2004Source
Journal of Statistical Planning and InferenceVolume
119Issue
1Pages
1-15Google Scholar check
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We consider the class of U-statistics which are based on a collection of associated random variables. Since independent random variables are associated, the class of U-statistics introduced by Hoeffding (Ann. Math. Statist. 19, 293-325) is included as a special case. Since many of the theoretical results which are valid for Hoeffding's U-statistics depend on the assumption of independence, the theory known cannot automatically be applied to the case of U-statistics based on associated random variables. In this paper, we prove a strong law of large numbers for this class of statistics in the case where the "kernel" of the U-statistic belongs to a large family of functions. © 2002 Elsevier B.V. All rights reserved.