A short note on resolving singularity problems in covariance matrices

Date

2012-01-01

Author

Purutçuoğlu Gazi, Vilda
Wit, Ernst

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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.

URI

https://hdl.handle.net/11511/88410

Journal

International Journal of Statistics and Probability

DOI

https://doi.org/10.5539/ijsp.v1n2p113

Collections

Department of Statistics, Article

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Citation Formats

V. Purutçuoğlu Gazi and E. Wit, “A short note on resolving singularity problems in covariance matrices,” International Journal of Statistics and Probability, pp. 113–118, 2012, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88410.