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Large Sample Properties of the Bayes' Sequential Procedure for Estimating the Arrival Rate of a Poisson Process with Invariant Loss

C. P. ShapiroRobert Wardrop

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

註釋

Let W sub n, n=0,1 ..., be the time until the nth arrival of a Poisson process with rate Theta. Using invariant loss L(Theta, Theta bar) =1/theta (Theta-Theta bar) squared and sampling costs involving cost per arrival and cost per unit time, the Bayes' sequential procedure (N*, Theta bar sub N*) is derived. The large sample properties of the procedure are then studied in the classical framework, and N*, the stopping time, is shown to be asymptotically equivalent to n*, the best fixed sample size procedure when Theta is known. Asymptotically normality of the sequential estimator Theta bar sub N* is also shown. (Author).