U-statistics with conditional kernels for incomplete data models

Ao Yuan (), Mihai Giurcanu (), George Luta () and Ming T. Tan ()
Additional contact information
Ao Yuan: Georgetown University
Mihai Giurcanu: University of Florida
George Luta: Georgetown University
Ming T. Tan: Georgetown University

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 2, No 2, 302 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10463-015-0537-6

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