الملخص الإنجليزي
The covariance matrix supports a variety of multivariate statistical analyses in both
theoretical and application areas of studies. Non-positive definite matrices often occur
with various causes such as the high dimensionality problem. In this study, three main
methods of covariance transformation assessed included; the vine, iterative transform
and the shrinkage method. To improve the performance of the shrinkage method, we
proposed two novel shrinkage targets: Target W (the Eigenvalue of the true covariance
matrix) and Target F (the Eigenvalue of the common target D).
Data on the number of patients recorded for 19 diseases in 11 governorates from the Oman
Ministry of Health were used to validate the proposed shrinkage targets. Preliminary
multivariate statistical tests on the data was done. The two proposed shrinkage targets
were assessed against the four existing common targets; A,B,C and D using the Frobenius
Norm and Shrinkage Intensity. In all validation tests, the proposed shrinkage targets
performed better than the existing common methods, showing improvements of the
shrinkage method to transform the non-positive definite covariance as applied to the
high dimensional disease data.
