Large Deviations Inequalities for Unequal Probability Sampling Without Replacement

TL;DR

This paper derives bounds on the tail probabilities for sampling without replacement where each element has a different probability of being selected, extending classical results to unequal probability scenarios.

Contribution

It introduces new large deviations inequalities for unequal probability sampling without replacement, a case not thoroughly addressed in prior work.

Findings

Established bounds on tail probabilities for unequal probability sampling

Extended classical inequalities to more general sampling schemes

Provided theoretical tools for analyzing sampling without replacement with unequal probabilities

Abstract

We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.