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

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  • Feng Yao
  • Carlos Martins-Filho

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.

Suggested Citation

  • Feng Yao & Carlos Martins-Filho, 2015. "An Asymptotic Characterization of Finite Degree U-statistics With Sample Size-Dependent Kernels: Applications to Nonparametric Estimators and Test Statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3251-3265, August.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:15:p:3251-3265
    DOI: 10.1080/03610926.2013.839037
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    Cited by:

    1. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.

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