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2009 Empirical measures for incomplete data with applications
Shojaeddin Chenouri, Majid Mojirsheibani, Zahra Montazeri
Electron. J. Statist. 3: 1021-1038 (2009). DOI: 10.1214/09-EJS420

Abstract

Methods are proposed to construct empirical measures when there are missing terms among the components of a random vector. Furthermore, Vapnik-Chevonenkis type exponential bounds are obtained on the uniform deviations of these estimators, from the true probabilities. These results can then be used to deal with classical problems such as statistical classification, via empirical risk minimization, when there are missing covariates among the data. Another application involves the uniform estimation of a distribution function.

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Shojaeddin Chenouri. Majid Mojirsheibani. Zahra Montazeri. "Empirical measures for incomplete data with applications." Electron. J. Statist. 3 1021 - 1038, 2009. https://doi.org/10.1214/09-EJS420

Information

Published: 2009
First available in Project Euclid: 13 October 2009

zbMATH: 1326.62206
MathSciNet: MR2557127
Digital Object Identifier: 10.1214/09-EJS420

Subjects:
Primary: 60G50 , 62G15
Secondary: 62H30

Keywords: ‎classification‎ , consistency , distribution function , Exponential bounds , Vapnik-Chervonenkis

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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