A Laplace-based model with flexible tail behavior

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2023-12-12 DOI:10.1016/j.csda.2023.107909

Cristina Tortora , Brian C. Franczak , Luca Bagnato , Antonio Punzo

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引用次数: 0

Abstract

The proposed multiple scaled contaminated asymmetric Laplace (MSCAL) distribution is an extension of the multivariate asymmetric Laplace distribution to allow for a different excess kurtosis on each dimension and for more flexible shapes of the hyper-contours. These peculiarities are obtained by working on the principal component (PC) space. The structure of the MSCAL distribution has the further advantage of allowing for automatic PC-wise outlier detection – i.e., detection of outliers separately on each PC – when convenient constraints on the parameters are imposed. The MSCAL is fitted using a Monte Carlo expectation-maximization (MCEM) algorithm that uses a Monte Carlo method to estimate the orthogonal matrix of eigenvectors. A simulation study is used to assess the proposed MCEM in terms of computational efficiency and parameter recovery. In a real data application, the MSCAL is fitted to a real data set containing the anthropometric measurements of monozygotic/dizygotic twins. Both a skewed bivariate subset of the full data, perturbed by some outlying points, and the full data are considered.

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具有灵活尾部行为的拉普拉斯模型

所提出的多重比例污染非对称拉普拉斯（MSCAL）分布是对多元非对称拉普拉斯分布的扩展，允许每个维度上不同的过量峰度和更灵活的超轮廓形状。这些特性都是通过在主成分（PC）空间工作而获得的。MSCAL 分布结构的另一个优点是，当对参数施加方便的约束条件时，可以自动检测 PC 中的离群值，即在每个 PC 上分别检测离群值。MSCAL 采用蒙特卡罗期望最大化（MCEM）算法拟合，该算法使用蒙特卡罗方法估计特征向量的正交矩阵。模拟研究用于评估所提出的 MCEM 在计算效率和参数恢复方面的效果。在真实数据应用中，MSCAL 适合于包含单卵/双卵双胞胎人体测量数据的真实数据集。既考虑了完整数据的偏斜双变量子集（受到一些离群点的扰动），也考虑了完整数据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]