The Annals of Statistics

Probabilities of Large Deviations for Empirical Measures

Gerald L. Sievers

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Abstract

Sanov's theorem on the asymptotic behavior of probabilities of large deviations for an empirical probability distribution is established under different conditions than previously given by Sanov, Hoadley and Stone. The new conditions are based on likelihood ratio approximations rather than on multinomial approximations. It is shown that these conditions are strictly more general than those of Stone.

Article information

Source
Ann. Statist., Volume 4, Number 4 (1976), 766-770.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343548

Digital Object Identifier
doi:10.1214/aos/1176343548

Mathematical Reviews number (MathSciNet)
MR415836

Zentralblatt MATH identifier
0367.60025

JSTOR
links.jstor.org

Subjects
Primary: 60F10: Large deviations
Secondary: 62F20 62G20: Asymptotic properties

Keywords
Large deviations exact slope empirical probability measures likelihood ratio

Citation

Sievers, Gerald L. Probabilities of Large Deviations for Empirical Measures. Ann. Statist. 4 (1976), no. 4, 766--770. doi:10.1214/aos/1176343548. https://projecteuclid.org/euclid.aos/1176343548


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