文章基本信息

标题：A Short Note on Resolving Singularity Problems in Covariance Matrices
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作者：Ezgi Ayyildiz ; Vilda Gazi ; Ernst Wit 等
期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2012
卷号：1
期号：2
页码：113
DOI：10.5539/ijsp.v1n2p113
出版社：Canadian Center of Science and Education
摘要：In problems where a distribution is concentrated in a lower-dimensional subspace, the covariance matrix faces a singularity problem. In downstream statistical analyzes this can cause a problem as the inverse of the covariance matrix is often required in the likelihood. There are several methods to overcome this challenge. The most well-known ones are the eigenvalue, singular value, and Cholesky decompositions. In this short note, we develop a new method to deal with the singularity problem while preserving the covariance structure of the original matrix. We compare our alternative with other methods. In a simulation study, we generate various covariance matrices that have different dimensions and dependency structures, and compare the CPU times of each approach.