Abstract

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 O(n−1/4logn) 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.

Details

Title
Uniformly asymptotic normality of sample quantiles estimator for linearly negative quadrant dependent samples
Author
Hu, Xueping 1   VIAFID ORCID Logo  ; Jiang, Rong 2 ; Yu, Keming 3 ; Zhang, Tong 4 

1  School of Mathematics and Computation Science, Anqing Normal University, Anqing, P.R. China; Department of Mathematics, Brunel University, Uxbridge, UK 
2  Department of Mathematics, Brunel University, Uxbridge, UK; Department of Mathematics, College of Sciences, Donghua University, Shanghai, P.R. China 
3  Department of Mathematics, Brunel University, Uxbridge, UK 
4  School of Mathematics and Computation Science, Anqing Normal University, Anqing, P.R. China 
Pages
1-12
Publication year
2018
Publication date
Jul 2018
Publisher
Springer Nature B.V.
ISSN
10255834
e-ISSN
1029242X
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13660-018-1788-6
ProQuest document ID
2077806509
Copyright
Journal of Inequalities and Applications is a copyright of Springer, (2018). All Rights Reserved., © 2018. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.