University of Washington - Statistics
Advisor: Jon Wellner
In this talk, we discuss exponential tail inequalities for the sum in the context of sampling without replacement. Using an exponential inequality due to Serfling as the basis for investigation, we consider the special case of sampling from a finite population containing only 0s and 1s. This leads to considering exponential bounds for the Hypergeometric distribution.
We present new exponential bounds for the tail of the Hypergeometric distribution, and compare these bounds to analogous results obtained for the Binomial distribution by several authors: Bennett, Kiefer, LeÃ³n and Perron, and Talagrand. We also compare a result due to Hoeffding to Serfling's exponential bound, and conjecture an improvement to Serfling's bound.
We conclude by connecting the Hypergeometric bounds to the two-sample problem, and presenting a new exponential bound for the two-sample Kolmogorov-Smirnov statistic when the two samples are of equal size.