Communications in Statistics - Simulation and Computation ( IF 0.9 ) Pub Date : 2020-09-29 , DOI: 10.1080/03610918.2020.1827265 Clécio S. Ferreira 1 , Heleno Bolfarine 2 , Víctor H. Lachos 3
Abstract
Scale mixtures of normal distributions are useful for statistical procedures involving symmetric and heavy-tailed data. Ferreira, Lachos, and Bolfarine (2016 Ferreira, C. S., V. H. Lachos, and H. Bolfarine. 2016. Likelihood-based inference for multivariate skew scale mixtures of normal distributions. AStA Advances in Statistical Analysis 100 (4):421–41. doi:10.1007/s10182-016-0266-z.[Crossref], [Web of Science ®] , [Google Scholar]) defined a multivariate skewed version of these distributions that offers much-needed flexibility by combining both skewness and heavy tails. In this work, we develop a linear mixed model based on skew scale mixtures of normal distributions, with emphasis on the skew Student-t normal, skew–slash and skew–contaminated normal distributions. Using the hierarchical structure of the model, we develop maximum likelihood estimation of the model parameters via the expectation-maximization (EM) algorithm. In addition, the standard errors are obtained via the approximate information matrix and the local influence analysis is explored under some perturbation schemes. To examine the performance and the usefulness of the proposed method, we present simulation studies and analyze a real dataset.
中文翻译:
基于正态分布的偏斜尺度混合的线性混合模型
摘要
正态分布的尺度混合对于涉及对称和重尾数据的统计过程很有用。Ferreira、Lachos 和 Bolfarine ( 2016 Ferreira、CS、VH Lachos和H. Bolfarine。2016 年。正态分布的多变量偏斜比例混合的基于可能性的推理。AStA 统计分析进展100 (4): 421 – 41。内政部:10.1007/s10182-016-0266-z。[交叉引用]、[Web of Science®]、 [谷歌学术搜索]) 定义了这些分布的多变量偏斜版本,它通过结合偏斜和重尾来提供急需的灵活性。在这项工作中,我们开发了一个基于正态分布的偏斜尺度混合的线性混合模型,重点是偏斜 Student - t正态分布、偏斜斜线和偏斜污染正态分布。使用模型的层次结构,我们通过期望最大化 (EM) 算法开发模型参数的最大似然估计。此外,通过近似信息矩阵获得标准误差,并在一些扰动方案下探索局部影响分析。为了检验所提出方法的性能和实用性,我们提出了模拟研究并分析了真实数据集。