Bayes sequential estimation for a Poisson process under a LINEX loss function |
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Authors: | Leng-Cheng Hwang Cheng-Hung Lee |
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Institution: | 1. Department of Statistics , Tunghai University , Taichung , Taiwan lchwang@thu.edu.tw;3. Department of Statistics , Tunghai University , Taichung , Taiwan |
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Abstract: | In this paper, within the framework of a Bayesian model, we consider the problem of sequentially estimating the intensity parameter of a homogeneous Poisson process with a linear exponential (LINEX) loss function and a fixed cost per unit time. An asymptotically pointwise optimal (APO) rule is proposed. It is shown to be asymptotically optimal for the arbitrary priors and asymptotically non-deficient for the conjugate priors in a similar sense of Bickel and Yahav Asymptotically pointwise optimal procedures in sequential analysis, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, CA, 1967, pp. 401–413; Asymptotically optimal Bayes and minimax procedures in sequential estimation, Ann. Math. Statist. 39 (1968), pp. 442–456] and Woodroofe A.P.O. rules are asymptotically non-deficient for estimation with squared error loss, Z. Wahrsch. verw. Gebiete 58 (1981), pp. 331–341], respectively. The proposed APO rule is illustrated using a real data set. |
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Keywords: | asymptotically non-deficient asymptotically optimal asymptotically pointwise optimal Bayes sequential estimation homogeneous Poisson process LINEX loss function |
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