Large Sample Theory for an Estimator of the Mean of a Counting Process with Panel Count Data by Jon

We study an estimator of the mean function of a counting process based on panel count data which has been proposed by Sun and Kalb eisch The setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly di erent times during a study Following a model proposed by Schick and Yu we allow the number of observation times and the observation times themselves to be random variables Our goal is to estimate the mean function of the counting process We show that the estimator of the mean function proposed by Sun and Kalb eisch can be viewed as a pseudo maximum likelihood estimator when a non homogeneous Poisson process model is assumed for the counting process We then show that the estimator of Sun and Kalb eisch is consistent and derive the pointwise asymptotic distribution for the estimator Research supported in part by National Science Foundation grant DMS and NIAID grant R AI Research supported in part by National Science Foundation grant DMS AMS subject classi cations Primary F F secondary J J