Sharp moderate and large deviations for sample quantiles

In this article, we discuss the sharp moderate and large deviations between the quantiles of population and the quantiles of samples. Cramér 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].