The Annals of Statistics

Erdos-Renyi Laws

Sandor Csorgo

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Abstract

Almost sure limit theorems are proved for maxima of functions of moving blocks of size $c \log n$ of independent rv's and for maxima of functions of the empirical probability measures of these blocks. It is assumed that for the functions considered a first-order large deviation statement holds. It is well known that the indices of these large deviations are, in most cases, expressible in terms of Kullback-Leibler information numbers, and the a.s. limits of the above maxima are the inverses of these indices evaluated at $1/c$. Several examples are presented as corollaries for frequently used test statistics and point estimators.

Article information

Source
Ann. Statist., Volume 7, Number 4 (1979), 772-787.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344727

Digital Object Identifier
doi:10.1214/aos/1176344727

Mathematical Reviews number (MathSciNet)
MR532241

Zentralblatt MATH identifier
0424.60032

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60F10: Large deviations 62B10: Information-theoretic topics [See also 94A17] 62G20: Asymptotic properties 62F20

Keywords
Strong limit theorems Erdos-Renyi maxima large deviations Kullback-Leibler information number test statistics point estimators

Citation

Csorgo, Sandor. Erdos-Renyi Laws. Ann. Statist. 7 (1979), no. 4, 772--787. doi:10.1214/aos/1176344727. https://projecteuclid.org/euclid.aos/1176344727


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