An Asymptotic Characterization of Finite Degree U-statistics With Sample Size-Dependent Kernels: Applications to Nonparametric Estimators and Test Statistics

Feng Yao and Carlos Martins-Filho

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 15, 3251-3265

Abstract: We provide a simple result on the H-decomposition of a U-statistics that allows for easy determination of its magnitude when the statistic’s kernel depends on the sample size n. The result provides a direct and convenient method to characterize the asymptotic magnitude of semiparametric and nonparametric estimators or test statistics involving high dimensional sums. We illustrate the use of our result in previously studied estimators/test statistics and in a novel nonparametric R2 test for overall significance of a nonparametric regression model.

Date: 2015
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DOI: 10.1080/03610926.2013.839037

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