Estimation of a counting model by the method of maximum partial and stratified likelihood

The author defines a counting model by giving the intensity function as a product of the basic intensity function and the regression function. The basic intensity depends on the calendar time and the number of previous jumps of the process while the regression function depends on temporal variables and an unknown parameter. The analogy with Cox’s model leads the author to estimate the parameter by the method of maximum likelihood, stratifying according to the number of previous jumps of the process. Asymptotic properties of the estimator are obtained using the results by Andersen and Gill. An application is presented.