Implementing and evaluating the nested maximum likelihood estimation technique

Estimating parameters describing response time distributions is difficult. The most commonly used method for parameter estimation is the maximum likelihood method (ML). However, this method applied on the three-parameter Weibull distribution returns biased estimates and the amount of bias is unknown. A recent method, that we call nested maximum likelihood, was proposed by Gourdin, Hansen and Jaumard (1994). Due to its complexity, it has never been used and tested systematically. Here I compare it to the maximum likelihood method. The results shows that nested maximum likelihood is slightly better than ML. Although the gains are marginal, the method has important implications for future research in parameter estimation.