## The Annals of Statistics

### Erdos-Renyi Laws

Sandor Csorgo

#### 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

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

#### 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