椭圆尾部的最大似然估计

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY Journal of Multivariate Analysis Pub Date : 2024-11-10 DOI:10.1016/j.jmva.2024.105382
Moosup Kim , Sangyeol Lee
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引用次数: 0

摘要

本研究的重点是椭圆尾部的有效估计。首先,我们推导出椭圆分布的频谱度量的密度函数,它涉及单位球面上的支配度量,从而得出椭圆尾部的密度函数。随后,我们根据推导出的密度函数类提出了最大似然估计法。由此得到的最大似然估计器(MLE)被证明是一致的,而且渐近正态。此外,该方法还证明了最大似然估计是渐近有效的,而且其渐近协方差矩阵可以用较低的计算成本进行估计。为了说明所提方法的有效性,还进行了模拟研究和实际数据分析。
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Maximum likelihood estimation of elliptical tail
This study is focused on the efficient estimation of the elliptical tail. Initially, we derive the density function of the spectral measure of an elliptical distribution concerning a dominating measure on the unit sphere, which consequently leads to the density function of the elliptical tail. Subsequently, we propose a maximum likelihood estimation based on the derived density function class. The resulting maximum likelihood estimator (MLE) is proven to be consistent and asymptotically normal. Moreover, it is demonstrated that the MLE is asymptotically efficient, with the added advantage that its asymptotic covariance matrix can be feasibly estimated at a low computational cost. A simulation study and real data analysis are conducted to illustrate the efficacy of the proposed method.
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来源期刊
Journal of Multivariate Analysis
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.
期刊最新文献
Maximum likelihood estimation of elliptical tail Covariance parameter estimation of Gaussian processes with approximated functional inputs PDE-regularised spatial quantile regression Diagnostic checking of periodic vector autoregressive time series models with dependent errors A conditional distribution function-based measure for independence and K-sample tests in multivariate data
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