Non-asymptotic bounds for inclusion probabilities in rejective sampling

TL;DR

This paper establishes non-asymptotic bounds for inclusion probabilities in rejective sampling, offering precise estimates for various sample sizes and matrix bounds for higher-order probabilities.

Contribution

It introduces new non-asymptotic bounds for inclusion probabilities and matrix inequalities in rejective sampling, advancing theoretical understanding.

Findings

Derived bounds for first and higher order inclusion probabilities.

Established semi-definite ordering bounds for matrices of inclusion probabilities.

Applicable to various size parameters in rejective sampling.

Abstract

We provide non-asymptotic bounds for first and higher order inclusion probabilities of the rejective sampling model with various size parameters. Further we derive bounds in the semi-definite ordering for matrices that collect (conditional) first and second order inclusion probabilities as their diagonal resp. off-diagonal entries.