Exponential inequalities for sampling designs
Statistics Theory
2020-10-26 v2 Statistics Theory
Abstract
In this work we introduce a general approach, based on the mar-tingale representation of a sampling design and Azuma-Hoeffding's inequality , to derive exponential inequalities for the difference between a Horvitz-Thompson estimator and its expectation. Applying this idea, we establish such inequalities for Chao's procedure, Till{\'e}'s elimination procedure, the generalized Midzuno method as well as for Brewer's method. As a by-product, we prove that the first three sampling designs are (conditionally) negatively associated. For such sampling designs, we show that that the inequality we obtain is usually sharper than the one obtained by applying known results for negatively associated random variables.
Cite
@article{arxiv.2006.16600,
title = {Exponential inequalities for sampling designs},
author = {Guillaume Chauvet and Mathieu Gerber},
journal= {arXiv preprint arXiv:2006.16600},
year = {2020}
}