Addressing non-normality in multivariate analysis using the t-distribution

IF 1.4 4区 数学 Q2 STATISTICS & PROBABILITY
Felipe Osorio, Manuel Galea, Claudio Henríquez, Reinaldo Arellano-Valle
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引用次数: 0

Abstract

The main aim of this paper is to propose a set of tools for assessing non-normality taking into consideration the class of multivariate t-distributions. Assuming second moment existence, we consider a reparameterized version of the usual t distribution, so that the scale matrix coincides with covariance matrix of the distribution. We use the local influence procedure and the Kullback–Leibler divergence measure to propose quantitative methods to evaluate deviations from the normality assumption. In addition, the possible non-normality due to the presence of both skewness and heavy tails is also explored. Our findings based on two real datasets are complemented by a simulation study to evaluate the performance of the proposed methodology on finite samples.

Abstract Image

利用t分布解决多元分析中的非正态性
本文的主要目的是提出一套评估非正态性的工具,同时考虑到多元 t 分布的类别。假定第二矩存在,我们考虑了通常 t 分布的重参数化版本,从而使尺度矩阵与分布的协方差矩阵重合。我们使用局部影响程序和库尔贝克-莱布勒发散度量,提出了评估正态性假设偏差的定量方法。此外,我们还探讨了由于偏斜和重尾的存在而可能导致的非正态性。我们基于两个真实数据集的研究结果通过模拟研究得到了补充,以评估所提出的方法在有限样本上的性能。
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来源期刊
Asta-Advances in Statistical Analysis
Asta-Advances in Statistical Analysis 数学-统计学与概率论
CiteScore
2.20
自引率
14.30%
发文量
39
审稿时长
>12 weeks
期刊介绍: AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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