رسائل ماجيستير
English
2020
Improved shrinkage method for high dimensional data
Ronald Wesonga, Afrah Darwish Sloom Al-Khumaisiyah , Ahmed Al-Hadhrami, Amadou Sarr
كلية العلوم-جامعة السلطان قابوس · عمان
The covariance matrix supports a variety of multivariate statistical analyses in both theoretical and applied areas of study. Non-positive definite matrices often occur due to various causes, such as the high-dimensionality problem. In this study, three main methods of covariance transformation were assessed: the vine method, the iterative transform, and the shrinkage method. To improve the performance of the shrinkage method, we proposed two novel shrinkage targets: Target W (the eigenvalues of the true covariance matrix) and Target F (the eigenvalues 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 were conducted. The two proposed shrinkage targets were assessed against 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, demonstrating improvements in the shrinkage method for transforming non-positive definite covariance matrices, as applied to high-dimensional disease data.