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U-statistics with conditional kernels for incomplete data models

  • Ao YuanEmail author
  • Mihai Giurcanu
  • George Luta
  • Ming T. Tan
Article
  • 300 Downloads

Abstract

For incomplete data models, the classical U-statistic estimator of a functional parameter of the underlying distribution cannot be computed directly since the data are not fully observed. To estimate such a functional parameter, we propose a U-statistic using a substitution estimator of the conditional kernel given the observed data. This kernel estimator is obtained by substituting the non-parametric maximum likelihood estimator for the underlying distribution function in the expression of the conditional kernel. We study the asymptotic properties of the proposed U-statistic for several incomplete data models, and in a simulation study, we assess the finite sample performance of the Mann–Whitney U-statistic with conditional kernel in the current status model. The analysis of a real-world data set illustrates the application of the proposed methods in practice.

Keywords

U-statistics Censored data Incomplete data models Non-parametric MLE 

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2015

Authors and Affiliations

  • Ao Yuan
    • 1
    Email author
  • Mihai Giurcanu
    • 2
  • George Luta
    • 1
  • Ming T. Tan
    • 1
  1. 1.Department of Biostatistics, Bioinformatics and BiomathematicsGeorgetown UniversityWashingtonUSA
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

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