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A robust two-stage procedure for the Poisson process under the linear exponential loss function

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  • Hwang, Leng-Cheng

Abstract

Within the framework of Bayesian model, we consider the problem of sequentially estimating the intensity parameter of a homogeneous Poisson process with linear exponential (LINEX) loss function and fixed cost per unit time. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem in this paper. The proposed two-stage procedure is robust in the sense that it does not depend on the prior. It is shown that the two-stage procedure shares the asymptotic properties with the asymptotically pointwise optimal procedures for a large class of the priors. A simulation study is conducted to compare the performances of the proposed two-stage procedure and the asymptotically pointwise optimal procedures.

Suggested Citation

  • Hwang, Leng-Cheng, 2020. "A robust two-stage procedure for the Poisson process under the linear exponential loss function," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220300766
    DOI: 10.1016/j.spl.2020.108773
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    References listed on IDEAS

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    1. Hwang, Leng-Cheng, 2018. "Second order optimal approximation in a particular exponential family under asymmetric LINEX loss," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 283-291.
    2. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
    3. Alicja Jokiel-Rokita, 2008. "Asymptotically pointwise optimal and asymptotically optimal stopping times in the Bayesian inference," Statistical Papers, Springer, vol. 49(2), pages 165-175, April.
    4. Nitis Mukhopadhyay & Sudeep R. Bapat, 2018. "Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1049-1075, October.
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