正相协下风险度量VaR样本分位数估计的渐近性质

THE ASYMPOTIC PROPERTIES OF THE SAMPLE QUANTILE ESTIMATOR OF VAR UNDER POSITIVE ASSOCIATED SAMPLES

本文研究了正相协严平稳样本下,风险度量VaR样本分位数估计的问题.利用其指数不等式和协方差不等式,获得了风险度量VaR的样本分位数估计的相合性和渐近正态性,并给出Bahadur表示.

In this paper,we consider the sample quantile estimator of VaR based on a stationary and positively associated sequence.For this setting,applying the exponential inequality of positively associated random variables,we prove the consistency and asympotic normality of the sample quantile estimator of VaR,and also give its Bahadur representation.