A comment on Heathcote, Brown, and Mewhort's QMLE method for response time distributions.

Heathcote, Brown, and Mewhort (2002) have introduced a new, robust method of estimating response time distributions. Their method may have practical advantages over conventional maximum likelihood estimation. The basic idea is that the likelihood of parameters is maximized given a few quantiles from the data. We show that Heathcote et al.'s likelihood function is not correct and provide the appropriate correction. However, although our correction stands on firmer theoretical ground than Heathcote et al.'s, it appears to yield worse parameter estimates. This result further indicates that, at least for some distributions and situations, quantile maximum likelihood estimation may have better nonasymptotic properties than a more theoretically justified approach.