Large Sample Theory for an
نویسندگان
چکیده
We study an estimator of the mean function of a counting process based on \panel count" data which has been proposed by Sun and Kalbbeisch (1995). 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 diierent times during a study. Following a model proposed by Schick and Yu (1997), 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 Kalbbeisch (1995) 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 Kalbbeisch (1995) is consistent, and derive the pointwise asymptotic distribution for the estimator.
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