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The Continuous Time Bayes' Sequential Procedure for Estimating the Arrival Rate of a Poisson Process and Large Sample Properties

C. P. ShapiroRobert Wardrop

出版	Defense Technical Information Center, 1977
URL	http://books.google.com.hk/books?id=CyM4OAAACAAJ&hl=&source=gbs_api

註釋

Let X(t), t> or = 0, be a homogeneous Poisson process with arrival rate Theta. Sequential estimation procedures (sigma, Theta bar sub sigma) are considered with loss due to estimation of L(Theta, Theta bar) = 1/Theta (Theta-Theta bar)squared, and sampling costs involving both time and arrival costs. In this context the Bayes', sequential procedure is obtained in a simple computable form. The large sample properties of the procedure are then studied when Theta is fixed but unknown, and the Bayes' stopping rule tau is shown to be asymptotically equivalent to the best fixed sample size procedure when Theta is known. Asymptotic normality of the Bayes' sequential estimator Theta bar sub tau of Theta is also shown. (Author).