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By Peter Guttorp, Peter Guttorp and Short Title


We consider iid homogeneous Poisson processes that are each stopped at some random time L i, independent of the history of the process. We observe at a fixed time to whether or not the process has been stopped, the number of events in (O,t O) and the time of the last event. We want to predict the termination times, and estimate the distribution of the L i. A method for unbi~sed prediction of L i is derived. This yields an inconsistent estimate of the distribution. A general consistent method for estimating the distribution is presented. In a special case it yields a maximum likehood estimate. The consistent estimate is not always preferrable in finite samples. KEYWORDS: Stopping time, prediction, minimum discrepancy estimation

Year: 1983
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