Non-parametric estimation of Expectation and Variance of event count and of incidence rate in a recurrent process -- where intensity of event-occurrence changes with the occurrence of each higher order event

In this paper, a novel non-parametric method for estimation of expectation and maximum value of the variance function is proposed for recurrent events where intensity of event occurrence changes with the occurrence of each higher order event. These kinds of recurrent events are often observed in clinical trials for cardio-vascular events and also in many social experiments involving drug addiction, armed robberies, etc. Simulated data is used to demonstrate the novel approach for estimating the mean and variance of such recurrent events and the results are compared with the result of Nelson Aalen estimator.