Asymptotic Properties of Conditional Maximum-Likelihood Estimators

Summary The problem of obtaining consistent estimates for structural parameters in the presence of infinitely many incidental parameters was discussed first by Neyman and Scott (1948). In this paper a maximum-likelihood method based on the conditional distribution given minimal sufficient statistics for the incidental parameters is suggested. It is proved that conditional maximum-likelihood estimates in the regular case are consistent and asymptotically normally distributed with a simple asymptotic variance. The efficiency problem of this new estimator is discussed in particular with respect to some situations with ancillary information.