多元广义双曲分布中偏度参数的假设检验

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Brazilian Journal of Probability and Statistics Pub Date : 2021-07-01 DOI:10.1214/21-BJPS502
M. Galea, F. Vilca, C. Zeller
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引用次数: 0

摘要

一类广义双曲型(GH)分布是由多元高斯分布和广义逆高斯分布的均值-方差混合产生的。这个丰富的GH分布家族包括一些著名的重尾和对称多元分布,包括正态反高斯分布和一些斜正态分布的比例混合分布家族的成员。一类GH分布在金融和信号处理应用中受到了相当大的关注。在本文中,我们提出了似然比(LR)检验来检验关于GH分布偏度参数的假设。由于似然函数的复杂性,EM算法在完整模型和简化模型中都能找到最大似然估计。出于比较的目的,由于其简单性,我们也考虑梯度(G)检验。仿真研究表明,LR和G测试通常能够达到期望的显著性水平,并且测试功率随着不对称性的增加而增加。本文开发的方法应用于两个实际数据集。
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Hypotheses tests on the skewness parameter in a multivariate generalized hyperbolic distribution
The class of generalized hyperbolic (GH) distributions is generated by a mean-variance mixture of a multivariate Gaussian with a generalized inverse Gaussian (GIG) distribution. This rich family of GH distributions includes some well-known heavy-tailed and symmetric multivariate distributions, including the Normal Inverse Gaussian and some members of the family of scale-mixture of skew-normal distributions. The class of GH distributions has received considerable attention in finance and signal processing applications. In this paper, we propose the likelihood ratio (LR) test to test hypotheses about the skewness parameter of a GH distribution. Due to the complexity of the likelihood function, the EM algorithm is used to find the maximum likelihood estimates both in the complete model and the reduced model. For comparative purposes and due to its simplicity, we also consider the Gradient (G) test. A simulation study shows that the LR and G tests are usually able to achieve the desired significance levels and the testing power increases as the asymmetry increases. The methodology developed in the paper is applied to two real datasets.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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