Cram\'{e}r-type large deviations for samples from a finite population

TL;DR

This paper establishes Cramér-type large deviation results for sample means from finite populations and extends these results to the finite population Student t-statistic, under weak conditions.

Contribution

It introduces Cramér-type large deviation principles for finite population means and Student t-statistics, expanding the theoretical understanding of their tail behaviors.

Findings

Large deviation results are comparable to self-normalized deviations for independent variables.

Results are established under weak conditions.

Extensions to the finite population Student t-statistic are provided.

Abstract

Cram\'{e}r-type large deviations for means of samples from a finite population are established under weak conditions. The results are comparable to results for the so-called self-normalized large deviation for independent random variables. Cram\'{e}r-type large deviations for the finite population Student $t$-statistic are also investigated.