Probabilistic Error Bounds for Simulation Quantile Estimators
分析了模拟分位数估计量误差概率的收敛速度，证明负相关抽样下指数收敛，分层估计量在有限样本下误差概率可为零，但样本量随维度指数增长。
Quantile estimation has become increasingly important, particularly in the financial industry, where value at risk (VaR) has emerged as a standard measurement tool for controlling portfolio risk. In this paper, we analyze the probability that a simulation-based quantile estimator fails to lie in a prespecified neighborhood of the true quantile. First, we show that this error probability converges to zero exponentially fast with sample size for negatively dependent sampling. Then we consider stratified quantile estimators and show that the error probability for these estimators can be guaranteed to be 0 with sufficiently large, but finite, sample size. These estimators, however, require sample sizes that grow exponentially in the problem dimension. Numerical experiments on a simple VaR example illustrate the potential for variance reduction.