During the course of this thesis, the Wallace and Freeman's 1987 second order MML approximation technique was taken apart and analysed. For some of the assumptions, improvements were suggested to improve the accuracy of the MML estimator.
A new MML approximation technique called MMLD was also implemented and investigated. The fourth-order extension to Wallace and Freeman's 1987 MML approximation technique was also derived for both univariate and multivariate distributions.
Experimental results has indicated that MMLD and fourth-order extension are both better MML estimators than Wallace and Freeman's 1987 estimate. However, the results are not conclusive and would require the use of SMML to settle it. The experiments also show that Wallace and Freeman 1987 with Observed Fisher deserves further attention.