重尾椭圆分布下的极值量级区域估计

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis Pub Date : 2024-03-20 DOI:10.1016/j.jmva.2024.105314

Jaakko Pere , Pauliina Ilmonen , Lauri Viitasaari

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引用次数: 0

摘要

考虑估算与极小概率相对应的极值量级区域。极值量分区域的估计很重要，但却很困难，因为极值区域只包含少数观测值或不包含观测值。在本文中，我们提出了一种针对重尾椭圆分布的仿射等变极端量级区域估计器。该估计器是通过扩展著名的单变量极值量级估计器来构建的。在估计位置和散度条件下，证明了估计器的一致性。通过模拟和真实数据示例说明了所开发估计器的实用性。

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On extreme quantile region estimation under heavy-tailed elliptical distributions

Consider the estimation of an extreme quantile region corresponding to a very small probability. Estimation of extreme quantile regions is important but difficult since extreme regions contain only a few or no observations. In this article, we propose an affine equivariant extreme quantile region estimator for heavy-tailed elliptical distributions. The estimator is constructed by extending a well-known univariate extreme quantile estimator. Consistency of the estimator is proved under estimated location and scatter. The practicality of the developed estimator is illustrated with simulations and a real data example.

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来源期刊

Journal of Multivariate Analysis 数学-统计学与概率论

CiteScore

2.40

自引率

25.00%

发文量

108

审稿时长

74 days

期刊介绍： Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.