Abstract
Conditions are given for almost certain and distribution convergence of self-normalized generalizedU-statistics composed of random variables without particular probabilistic structure. The set of almost certain limit points of some classicalU-statistics is obtained. A variant of theU-statistic involving squares of some of the random variables is also treated. Applications include Martingale differences, stationary sequences, and the classical i.i.d. case where a Marcinkiewicz-Zygmund-type strong law is obtained.
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Teicher, H. Convergence of self-normalized generalizedU-statistics. J Theor Probab 5, 391–405 (1992). https://doi.org/10.1007/BF01046743
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DOI: https://doi.org/10.1007/BF01046743