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

Abstract

We reconsider the efficiency bound for the semi-parametric Mixed Proportional Hazard (MPH) model with parametric baseline hazard and regression function, but unspecified distribution of multiplicative unobserved heterogeneity. We show that the efficient score has a singular distribution if and only if the baseline hazard is Weibull type. A sufficient condition for nonsingularity of the distribution is that the baseline hazard is bounded from zero and infinity in zero.