ABSTRACT On the basis of a sample of either independent, identically distributed or possibly weakly dependent and stationary random variables from an unknown model F with a heavy right-tail function, and for any small level q, the value-at-risk (VaR) at the level q, i.e. the size of the loss that occurs with a probability q, is estimated by new semi-parametric reduced-bias procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p an adequate real number. After a brief reference to the asymptotic properties of these new VaR-estimators, we proceed to an overall comparison of alternative VaR-estimators, for finite samples, through large-scale Monte-Carlo simulation techniques. Possible algorithms for an adaptive VaR-estimation, an application to financial data and concluding remarks are also provided.

中文翻译：

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减少偏差和部分减少偏差的均值 p 值风险估计：蒙特卡罗比较和应用

摘要 基于来自具有重右尾函数的未知模型 F 的独立、同分布或可能弱相关且平稳的随机变量的样本，以及对于任何小水平 q，风险价值 (VaR)在 q 级，即以概率 q 发生的损失大小，由新的半参数减少偏差程序估计，基于一组 k 个高阶统计商的均值 p， p 是一个足够的实数。在简要参考这些新 VaR 估计量的渐近特性后，我们通过大规模蒙特卡罗模拟技术对有限样本的替代 VaR 估计量进行了全面比较。还提供了自适应 VaR 估计的可能算法、财务数据的应用和结束语。