正相协样本分位数估计的Bahadur表示

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

作为一类常见的随机变量序列,正相协随机变量序列在可靠性理论和多元统计分析中有着广泛应用.本文的主要目的是研究一类严平稳正相协随机样本分位数的估计问题.首先,利用正相协随机序列的性质,我们获得了一个有关正相协随机变量的协方差不等式.然后,利用正相协序列的指数不等式获得了一个有关经验分布函数的不等式.最后,我们利用所得不等式,在适当的条件下,进一步讨论了样本分位数估计的强相合性,并给出了其Bahadur表示及其收敛速度.

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.