Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior

Marek Męczarski; Ryszard Zieliński

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 4, page 457-463
  • ISSN: 1233-7234

Abstract

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A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.

How to cite

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Męczarski, Marek, and Zieliński, Ryszard. "Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior." Applicationes Mathematicae 24.4 (1997): 457-463. <http://eudml.org/doc/219185>.

@article{Męczarski1997,
abstract = {A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.},
author = {Męczarski, Marek, Zieliński, Ryszard},
journal = {Applicationes Mathematicae},
keywords = {prior distribution uncertainty; homogeneous Poisson process; LINEX loss function; LINEX loss},
language = {eng},
number = {4},
pages = {457-463},
title = {Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior},
url = {http://eudml.org/doc/219185},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Męczarski, Marek
AU - Zieliński, Ryszard
TI - Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 4
SP - 457
EP - 463
AB - A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.
LA - eng
KW - prior distribution uncertainty; homogeneous Poisson process; LINEX loss function; LINEX loss
UR - http://eudml.org/doc/219185
ER -

References

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  1. J. O. Berger (1994), An overview of robust Bayesian analysis, Test 3, 5-124. Zbl0827.62026
  2. A. DasGupta and W. J. Studden (1991), Robust Bayesian experimental design in normal linear models, Ann. Statist. 19, 1244-1256. Zbl0744.62099
  3. N. Ebrahimi, (1992), An optimal stopping time for a power law process, Sequential Anal. 11, 213-227. Zbl0766.62049
  4. M. Męczarski and R. Zieliński (1991), Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior, Statist. Probab. Lett. 12, 329-333. 
  5. M. Męczarski and R. Zieliński (1997), Stability of the posterior mean in linear models: an admissibility property of D-optimum and E-optimum designs, ibid., to appear. Zbl0902.62084
  6. S. Sivaganesan and J. O. Berger (1989), Ranges of posterior measures for priors with unimodal contaminations, Ann. Statist. 17, 868-889. Zbl0724.62032
  7. A. Zellner (1986), Bayesian estimation and prediction using asymmetric loss functions, J. Amer. Statist. Assoc. 81, 446-451. Zbl0603.62037

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