On perturbations of strongly admissible prior distributions

Morris L. Eaton; James P. Hobert; Galin L. Jones

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 5, page 633-653
  • ISSN: 0246-0203

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Eaton, Morris L., Hobert, James P., and Jones, Galin L.. "On perturbations of strongly admissible prior distributions." Annales de l'I.H.P. Probabilités et statistiques 43.5 (2007): 633-653. <http://eudml.org/doc/77949>.

@article{Eaton2007,
author = {Eaton, Morris L., Hobert, James P., Jones, Galin L.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Dirichlet form; estimation; formal Bayes rule; formal posterior distribution; improper prior distribution; irreducibility; symmetric Markov chain; recurrence; restricted parameter space},
language = {eng},
number = {5},
pages = {633-653},
publisher = {Elsevier},
title = {On perturbations of strongly admissible prior distributions},
url = {http://eudml.org/doc/77949},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Eaton, Morris L.
AU - Hobert, James P.
AU - Jones, Galin L.
TI - On perturbations of strongly admissible prior distributions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 5
SP - 633
EP - 653
LA - eng
KW - Dirichlet form; estimation; formal Bayes rule; formal posterior distribution; improper prior distribution; irreducibility; symmetric Markov chain; recurrence; restricted parameter space
UR - http://eudml.org/doc/77949
ER -

References

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  2. [2] L.D. Brown, Fundamentals of Statistical Exponential Families with Applications to Statistical Decision Theory, Institute of Mathematical Statistics, Hayward, CA, 1986. Zbl0685.62002MR882001
  3. [3] K.L. Chung, W.H.J. Fuchs, On the distribution of values of sums of random variables, Memoirs of the American Mathematical Society6 (1951) 1-12. Zbl0042.37502MR40610
  4. [4] M.L. Eaton, A method for evaluating improper prior distributions, in: Gupta S.S., Berger J.O. (Eds.), Statistical Decision Theory and Related Topics III, vol. 1, Academic Press, Inc., New York, 1982. Zbl0581.62005MR705296
  5. [5] M.L. Eaton, A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains, Annals of Statistics20 (1992) 1147-1179. Zbl0767.62002MR1186245
  6. [6] M.L. Eaton, Admissibility in quadratically regular problems and recurrence of symmetric Markov chains: Why the connection?, Journal of Statistical Planning and Inference64 (1997) 231-247. Zbl0944.62010MR1621615
  7. [7] M.L. Eaton, Markov chain conditions for admissibility in estimation problems with quadratic loss, in: de Gunst M., Klaassen C., van der Vaart A. (Eds.), State of the Art in Probability and Statistics – A Festschrift for Willem R. van Zwet, The IMS Lecture Notes Series, vol. 36, IMS, Beachwood, OH, 2001. 
  8. [8] M.L. Eaton, Evaluating improper priors and the recurrence of symmetric Markov chains: An overview, in: Dasgupta A. (Ed.), A Festschrift to Honor Herman Rubin, The IMS Lecture Notes Series, vol. 45, IMS, Beachwood, OH, 2004. Zbl1268.62010MR2126883
  9. [9] J.P. Hobert, D. Marchev, J. Schweinsberg, Stability of the tail Markov chain and the evaluation of improper priors for an exponential rate parameter, Bernoulli10 (2004) 549-564. Zbl1049.60068MR2061443
  10. [10] J.P. Hobert, C.P. Robert, Eaton’s Markov chain, its conjugate partner and P -admissibility, Annals of Statistics27 (1999) 361-373. Zbl0945.62012MR1701115
  11. [11] J.P. Hobert, J. Schweinsberg, Conditions for recurrence and transience of a Markov chain on Z + and estimation of a geometric success probability, Annals of Statistics30 (2002) 1214-1223. Zbl1103.60315MR1926175
  12. [12] I. Johnstone, Admissibility, difference equations and recurrence in estimating a Poisson mean, Annals of Statistics12 (1984) 1173-1198. Zbl0557.62006MR760682
  13. [13] I. Johnstone, Admissible estimation, Dirichlet principles and recurrence of birth-death chains on Z + p , Probability Theory and Related Fields71 (1986) 231-269. Zbl0592.62009MR816705
  14. [14] W.-L. Lai, Admissibility and the recurrence of Markov chains with applications, Ph.D. thesis, University of Minnesota, 1996. 
  15. [15] S.P. Meyn, R.L. Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993. Zbl0925.60001MR1287609

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