Sharp moderate and large deviations for sample quantiles

TL;DR

This paper investigates the precise probabilities of deviations between population and sample quantiles, refining existing deviation principles through Cramér and Bahadur-Rao type results under mild conditions.

Contribution

It introduces sharper moderate and large deviation results for sample quantiles, extending and refining previous deviation principles by Xu and Miao.

Findings

Established Cramér type moderate deviations for sample quantiles.

Derived Bahadur-Rao type large deviations with mild conditions.

Refined existing deviation principles for quantiles.

Abstract

In this article, we discuss the sharp moderate and large deviations between the quantiles of population and the quantiles of samples. Cram\'{e}r type moderate deviations and Bahadur-Rao type large deviations are established with some mild conditions. The results refine the moderate and large deviation principles of Xu and Miao [Filomat 2011; 25(2): 197-206].