A Short Note on Resolving Singularity Problems in Covariance Matrices


  •  Ezgi Ayyildiz    
  •  Vilda Gazi    
  •  Ernst Wit    

Abstract

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.


This work is licensed under a Creative Commons Attribution 4.0 License.
  • Issn(Print): 1927-7032
  • Issn(Onlne): 1927-7040
  • Started: 2012
  • Frequency: bimonthly

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