Maximal likelihood estimation of correlation matrix under inequality constraints and Gibbs sampling

Research Report SRR98-005

Maximal likelihood estimation of correlation matrix under inequality constraints and Gibbs sampling

Toshio Sakata and Ryuichi Sawae

Abstract: The maximum likelihood estimation of correlation matrix under order restriction among correlations is treated. Two maximization process (A) maximization with respect to correlation matrix and (B) maximization with respect to variance are iterated. For the maximization process (A) we generate uniformly distributed random correlation matrices on the hypothesis space by Gibbs sampling. In the maximization process (B) we show that the maximum point is the fixed point of the iterative application of a certain non-linear function. A simulation result is given which compares the relative errors of the mle and other competetives.

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