Abstract

In this paper, we consider principal component analysis for α-stable random vectors. First, we present a new measure of dependence for bivariate α-stable vectors. The introduced measure is distribution based, symmetric, and linear in its arguments, and it measures the dispersion of an α-stable random variable. Then, using the proposed measure, we define principal components for α-stable vectors such that they contain the total variation of data. The new proposed method enables us to describe the variation of data by a few principal components. In the presented method, we seek linear combinations which have the largest shares of scale parameters of the original variables. Using numerical examples, we demonstrate the efficiency of the proposed analysis.

摘要

在本文中，我们考虑对α稳定的随机向量进行主成分分析。首先，我们提出了一种新的衡量双变量α稳定向量相关性的方法。引入的度量是基于分布的、对称的和线性的，它度量了一个α稳定随机变量的离散度。然后，使用建议的度量，我们定义α的主成分- 稳定的向量，使它们包含数据的总变化。新提出的方法使我们能够通过几个主成分来描述数据的变化。在所提出的方法中，我们寻求在原始变量的尺度参数中所占份额最大的线性组合。使用数值示例，我们证明了所提出的分析的效率。