Modified maximum likelihood estimation
The problems raised by Chan (1982) of modified maximum likelihood estimation (MMLE) are considered. Using sample moments to reduce the number of parameters in the likelihood function of a statistical model under certain kind of reparametrization, we obtained the MMLE estimates by locating an optimal solution in the reduced parameter space. Conditions under which the MMLE gives consistent and asymptotically normal estimators areconsidered. For symmetric location–scale families, the MMLE for the shape parameter is asymptotically efficient. We also examine an example of twoparameter Weibull distribution on failure times data.