Empirical measures for incomplete data with applications
Shojaeddin Chenouri, Majid Mojirsheibani, and Zahra Montazeri
Source: Electron. J. Statist.
Volume 3
(2009), 1021-1038.
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.
Primary Subjects: 60G50, 62G15
Secondary Subjects: 62H30
Keywords: Exponential bounds; Vapnik-Chervonenkis; distribution function; classification; consistency
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ejs/1255440399
Digital Object Identifier: doi:10.1214/09-EJS420
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