On perturbations of strongly admissible prior distributions

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 43, Issue 5, 2007, Pages 633-653

  Eaton, Morris L ^a   Hobert, James P ^b   Jones, Galin L ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b University of Florida   (United States)

Author keywords

Admissibility; Dirichlet form; Estimation; Formal Bayes rule; Formal posterior distribution; Improper prior distribution; Irreducibility; Recurrence; Restricted parameter space; Symmetric Markov chain

Indexed keywords

EID: 34547186561     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2006.09.006     Document Type: Article

References (15)

1. Brown L.D. Admissible estimators, recurrent diffusions, and insoluble boundary value problems. Annals of Mathematical Statistics 42 (1971) 855-904
2. Brown L.D. Fundamentals of Statistical Exponential Families with Applications to Statistical Decision Theory (1986), Institute of Mathematical Statistics, Hayward, CA
3. Chung K.L., and Fuchs W.H.J. On the distribution of values of sums of random variables. Memoirs of the American Mathematical Society 6 (1951) 1-12
4. Eaton M.L. A method for evaluating improper prior distributions. In: Gupta S.S., and Berger J.O. (Eds). Statistical Decision Theory and Related Topics III, vol. 1 (1982), Academic Press, Inc., New York
5. Eaton M.L. A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains. Annals of Statistics 20 (1992) 1147-1179
6. Eaton M.L. Admissibility in quadratically regular problems and recurrence of symmetric Markov chains: Why the connection?. Journal of Statistical Planning and Inference 64 (1997) 231-247
7. Eaton M.L. Markov chain conditions for admissibility in estimation problems with quadratic loss. In: de Gunst M., Klaassen C., and 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 (2001), IMS, Beachwood, OH
8. Eaton M.L. 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 (2004), IMS, Beachwood, OH
9. Hobert J.P., Marchev D., and Schweinsberg J. Stability of the tail Markov chain and the evaluation of improper priors for an exponential rate parameter. Bernoulli 10 (2004) 549-564
10. Hobert J.P., and Robert C.P. Eaton's Markov chain, its conjugate partner and P-admissibility. Annals of Statistics 27 (1999) 361-373
11. + and estimation of a geometric success probability. Annals of Statistics 30 (2002) 1214-1223
12. Johnstone I. Admissibility, difference equations and recurrence in estimating a Poisson mean. Annals of Statistics 12 (1984) 1173-1198
13. p. Probability Theory and Related Fields 71 (1986) 231-269
14. W.-L. Lai, Admissibility and the recurrence of Markov chains with applications, Ph.D. thesis, University of Minnesota, 1996
15. Meyn S.P., and Tweedie R.L. Markov Chains and Stochastic Stability (1993), Springer-Verlag, London