Asymptotic distribution of certain degenerate V- and U-statistics with estimated parameters

Abstract

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems.

Revised proof of Theorem 1; other minor changes in text

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• Asymptotics for non-degenerate multivariate $U$-statistics with estimated nuisance parameters under the null and local alternative hypotheses