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.
Publié le : 1979-07-14
Classification:
Strong limit theorems,
Erdos-Renyi maxima,
large deviations,
Kullback-Leibler information number,
test statistics,
point estimators,
60F15,
60F10,
62B10,
62G20,
62F20
@article{1176344727,
author = {Csorgo, Sandor},
title = {Erdos-Renyi Laws},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 772-787},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344727}
}
Csorgo, Sandor. Erdos-Renyi Laws. Ann. Statist., Tome 7 (1979) no. 1, pp. 772-787. http://gdmltest.u-ga.fr/item/1176344727/