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A formulation for continuous mixtures of multivariate normal distributions
Journal of Multivariate Analysis ( IF 1.6 ) Pub Date : 2021-06-12 , DOI: 10.1016/j.jmva.2021.104780
Reinaldo B. Arellano-Valle , Adelchi Azzalini

Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal variable, by changing the nature of these basic constituents from constants to random quantities. More recently, other mixture-type constructions have been introduced, where the core random component, on which the mixing operation operates, is not necessarily normal. The main aim of the present work is to show that many existing constructions can be encompassed by a formulation where normal variables are mixed using two univariate random variables. For this formulation, we derive various general properties, with focus on the multivariate context. Within the proposed framework, it is also simpler to formulate new proposals of parametric families, and we provide a few such instances. As a side product, the exposition provides a concise compendium of the main constructions of continuous normal-mixtures type, although a full overview of this vast theme is not attempted.



中文翻译:

多元正态分布的连续混合公式

文献中长期存在几种形式的正态变量的连续混合形式,其中混合变量对多元正态变量的均值或方差或均值和方差进行操作,通过改变这些基本变量的性质成分从常数到随机量。最近,引入了其他混合型结构,其中混合操作所依赖的核心随机成分不一定是正常的。目前工作的主要目的是表明许多现有结构可以包含在一个公式中,其中使用两个单变量随机变量混合正态变量。对于这个公式,我们推导出各种一般属性,重点是多变量上下文。在提议的框架内,制定参数族的新建议也更简单,我们提供了一些这样的例子。作为副产品,该说明提供了连续正态混合类型主要结构的简明概要,尽管没有尝试对这个庞大的主题进行全面概述。

更新日期:2021-06-21
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