极值的概率匹配预测
Probability-Matching Predictors for Extreme Extremes
摘要：
一个位置和规模不变的预测器构造，表现出良好的概率匹配的极端预测以外的跨度从各种（固定）一般分布的数据。它是通过三参数{μ，σ，σ}广义帕累托分布（GPD）构造的。预测器的目的是提供匹配概率正好为GPD在极端重尾极限和极端有界尾极限，同时给出了一个很好的近似概率匹配在所有中间值的尾部参数λ。该预测器即使对于小样本量N也是有效的，甚至小到N = 3。本文的主要目的是提出一些冗长的推导，其中大量借鉴理论的超几何函数，特别是劳里切拉函数。虽然建设的灵感来自贝叶斯方法的预测问题，它考虑了模糊的先验信息的情况下，参数和模型，所有的推导进行使用抽样论。
英文摘要：
A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the three-parameter {μ, σ, ξ} Generalized Pareto Distribution (GPD). The predictor is designed to provide matching probability exactly for the GPD in both the extreme heavy-tailed limit and the extreme bounded-tail limit, whilst giving a good approximation to probability matching at all intermediate values of the tail parameter ξ. The predictor is valid even for small sample sizes N, even as small as N = 3. The main purpose of this paper is to present the somewhat lengthy derivations which draw heavily on the theory of hypergeometric functions, particularly the Lauricella functions. Whilst the construction is inspired by the Bayesian approach to the prediction problem, it considers the case of vague prior information about both parameters and model, and all derivations are undertaken using sampling theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
