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Estimation of multivariate conditional-tail-expectation using Kendall's process

机译:使用肯德尔过程估计多元条件尾部期望

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This paper deals with the problem of estimating the multivariate version of the Conditional-Tail-Expectation, proposed by Di Bernardino et al. [(2013), 'Plug-in Estimation of Level Sets in a Non-Compact Setting with Applications in Multivariable Risk Theory', ESAIM: Probability and Statistics, (17), 236-256]. We propose a new nonparametric estimator for this multivariate risk-measure, which is essentially based on Kendall's process [Genest and Rivest, (1993), 'Statistical Inference Procedures for Bivariate Archimedean Copulas', Journal of American Statistical Association, 88(423), 1034-1043]. Using the central limit theorem for Kendall's process, proved by Barbe et al. [(1996), 'On Kendall's Process', Journal of Multivariate Analysis, 58(2), 197-229], we provide a functional central limit theorem for our estimator. We illustrate the practical properties of our nonparametric estimator on simulations and on two real test cases. We also propose a comparison study with the level sets-based estimator introduced in Di Bernardino et al. [(2013), 'Plug-In Estimation of Level Sets in A Non-Compact Setting with Applications in Multivariable Risk Theory', ESAIM: Probability and Statistics, (17), 236-256] and with (semi-)parametric approaches.
机译:本文讨论了Di Bernardino等人提出的估计条件尾部期望的多元版本的问题。 [(2013),“非紧凑环境中水平集的插入估计及其在多变量风险理论中的应用”,ESAIM:概率与统计,(17),236-256]。我们为此多元风险度量提出了一种新的非参数估计量,该估计量主要基于肯德尔的过程[Genest和Rivest,(1993),“双变量Archimedean Copulas的统计推断程序”,美国统计协会杂志,88(423), 1034-1043]。 Barbe等人证明了使用Kendall过程的中心极限定理。 [(1996),“关于肯德尔的过程”,《多元分析杂志》,58(2),197-229],我们为估计器提供了一个功能性中心极限定理。我们在仿真和两个实际测试用例上说明了非参数估计器的实用属性。我们还提议与Di Bernardino等人引入的基于水平集的估计量进行比较研究。 [(2013),“非紧凑环境中水平集的插入式估计及其在多变量风险理论中的应用”,ESAIM:概率与统计,(17),236-256]和(半)参数方法。

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