On the Berry-Esseen bound for the Student statistic

TL;DR

This paper derives explicit Berry-Esseen bounds for the Student statistic and self-normalized sums, providing clearer quantification of their distributional convergence and comparing these bounds with existing results.

Contribution

It introduces new Berry-Esseen bounds with explicit constants for the Student statistic and self-normalized sums, enhancing understanding of their distributional accuracy.

Findings

New bounds with explicit constants are established.

The bounds are compared favorably with existing results.

Results improve the quantification of convergence rates for the Student statistic.

Abstract

New Berry--Esseen-type bounds, with explicit constant factors, for the distribution of the Student statistic and, equivalently, for that of the self-normalized sum of independent zero-mean random variables are obtained. These bounds are compared with the corresponding existing results.