Appraisals on Resolving Singularity Problem of Covariance matrix in High Dimension

Hafeez Ahmed, Maznah Mat Kasim, Malina Zulkifli

Abstract


This is an expository essay that reviews the recent developments on resolving the singularity problem in the variance/covariance matrix in high dimension. Furthermore, the interrelated and multidimensional linear relationships between columns or rows in the covariance matrix structure result into zero determinants in its computations and are singular. This also means that the inverse of the underlying matrix becomes inflexible, that leads to a computational problem in the likelihood. Therefore, this paper intent to review some of the literatures in resolving the singularity problems and also to evaluate some of the methods used. This study is very vital since it will resolve major problems in many areas such as functional magnetic resonance imaging analysis of gene expression arrays, risk management and portfolio allocation.


Keywords


Multivariate analysis, High dimension, Covariance structure and Singularity problem

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