Electronic Journal of Statistics

Empirical measures for incomplete data with applications

Shojaeddin Chenouri, Majid Mojirsheibani, and Zahra Montazeri

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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.

Article information

Electron. J. Statist., Volume 3 (2009), 1021-1038.

First available in Project Euclid: 13 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks 62G15: Tolerance and confidence regions
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Exponential bounds Vapnik-Chervonenkis distribution function classification consistency


Chenouri, Shojaeddin; Mojirsheibani, Majid; Montazeri, Zahra. Empirical measures for incomplete data with applications. Electron. J. Statist. 3 (2009), 1021--1038. doi:10.1214/09-EJS420. https://projecteuclid.org/euclid.ejs/1255440399

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