## The Annals of Probability

### Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm

Kenneth S. Alexander

#### Abstract

Sharp exponential bounds for the probabilities of deviations of the supremum of a (possibly non-iid) empirical process indexed by a class $\mathscr{F}$ of functions are proved under several kinds of conditions on $\mathscr{F}$. These bounds are used to establish laws of the iterated logarithm for this supremum and to obtain rates of convergence in total variation for empirical processes on the integers.

#### Article information

Source
Ann. Probab., Volume 12, Number 4 (1984), 1041-1067.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993141

Digital Object Identifier
doi:10.1214/aop/1176993141

Mathematical Reviews number (MathSciNet)
MR757769

Zentralblatt MATH identifier
0549.60024

JSTOR