The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model

We reconsider the efficiency bound for the semi-parametric Mixed Proportional Hazard (MPH) model with parametric baseline hazard and regression function. This bound was first derived by Hahn (1994). One of his results is that if the baseline hazard is Weibull, the efficiency bound is singular, even if the model is semi-parametrically identified. This implies that neither the Weibull parameter nor the regression coefficients can be estimated at the root N rate. We show that Hahn's results are confined to a class of models that is closed under the power transformation. The Weibull model is the most prominent model of this class. We also present a new nonparametric identification result. This identification results allows for infinite mean of the mixing distribution and ensures that the efficiency bound is nonsingular. This implies that root N estimation is possible.