A non-stationary Cox model

The purpose of this paper is to consider the problem of statistical inferen ce about a hazard late function that is specified as the product of a param etric regression part and a non-parametric baseline hazard. Unlike Cox's pr oportional hazard model, the baseline hazard not only depends on the durati on variable, hut also on the starting date of the phenomenon of interest. W e propose a new estimator of the regression parameter which allows for non- stationarity in the hazard rate. We show that it is asymptotically normal a t root-n and that its asymptotic variance attains the information bound for estimation of the regression coefficient. We also consider an estimator of the integrated baseline hazard, and determine its asymptotic properties. T he finite sample performance of our estimators are studied.