THE EFFICIENCY BOUND OF THE MIXED PROPORTIONAL HAZARD MODEL

The semiparametric efficiency bound of the mixed proportional hazard m odel is derived. The density of the model factors in such a way that t here exists a complete sufficient statistic for the individual heterog eneity. The efficient score is shown to be the difference between the score in the parametric direction and its conditional expectation give n the sufficient statistic. Applying this result to the single-spell W eibull mixed proportional hazard model, it is shown that its informati on matrix is singular and there cannot exist any square-root n-consist ent estimator sequence. The information of the multi-spell Weibull mix ed proportional hazard model is shown to be nonsingular in general.