On the invariance principle for U-statistics

Peter Hall

Stochastic Processes and their Applications, 1979, vol. 9, issue 2, 163-174

Abstract: Let Tn be a U-statistic and Sn its projection (in the sense of Hájek). Limit theory for U-statistics is usually considered in two disjoint cases, termed degenerate and nondegenerate. The traditional method is to treat the cases separately, using different techniques in each to obtain a solution. Here we present a unified treatment based on a joint invariance principle for the vector (Tn, Tn - Sn), from which the invariance principles in both the degenerate and nondegenerate cases follow as easy corollaries.

Keywords: U-statistics; invariance; principle; projection; degenerate; and; nondegenerate (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (4)

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