Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (4): 524-532.doi: 10.3969/j.issn.1005-3085.2015.04.006

Previous Articles     Next Articles

The Bahadur Representation for the Estimator of Sample Quantiles under Positive Associated Samples

LI Yong-ming1,   ZHANG Wen-ting2,   LI Nai-yi3,   YAO Jing4   

  1. 1- School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001
    2- Laibin Campus, Guilin University of Aerospace Technology, Laibin 546100
    3- College of Science, Guangdong Ocean University, Zhanjiang 524088
    4- College of Mathematical Science, Guangxi Teachers Education University, Nanning 530023
  • Received:2014-01-09 Accepted:2014-10-09 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The National Natural Science Foundation of China (11461057); the Natural Science Foundation of Jiangxi Province (20122BAB201007); the Natural Science Foundation of the Education Department of Jiangxi Province (GJJ12604).

Abstract:

The positively associated sequence is a general class of random variables, and has been widely utilized in multivariate statistical analysis and system reliability. The purpose of this paper is to estimate sample quantiles based on a stationary and positively associated sequ-ence. By applying the property of a positively associated sequence, we establish a covariance inequality for the positively associated variables. And then, by using the exponential inequality of a positively associated sequence, we obtain an inequality for the empirical distribution function. Furthermore, under certain conditions, by virtue of the obtained inequality, we discuss the consistency of the sample quantile estimator for positively associated sequence, and derive the Bahadur representation together with its convergence rate.

Key words: positive associated sequence, sample quantiles, Bahadur representation

CLC Number: