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In the present article, by utilizing some inequalities for linearly negative quadrant dependent random variables, we discuss the uniformly asymptotic normality of sample quantiles for linearly negative quadrant dependent samples under mild conditions. The rate of uniform asymptotic normality is presented and the rate of convergence is near    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$O(n^{-1/4} \log n)$\end{document}   O  (   n   −  1  /  4    log  n  )when the third moment is finite, which extends and improves the corresponding results of Yang et al. (J. Inequal. Appl. 2011:83,  2011 ) and Liu et al. (J. Inequal. Appl. 2014:79,  2014 ) under negatively associated random samples in some sense.

Uniformly asymptotic normality of sample quantiles estimator for linearly negative quadrant dependent samples