Interval estimation in exponential families

Statistica Sinica

Volumn 13, Issue 1, 2003, Pages 19-49

  Brown, Lawrence D ^a   Cai, T Tony ^a   DasGupta, Anirban ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Bayes; Binomial distribution; Confidence intervals; Coverage probability; Edgeworth expansion; Expected length; Jeffreys prior; Natural exponential family; Negative binomial distribution; Normal approximation; Poisson distribution; Quadratic variance function

Indexed keywords

EID: 0038374833     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. Agresti, A. and Coull, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. Amer. Statist. 52, 119-126.
2. Barndorff-Nielsen, O. E. and Cox, D. R. (1989). Asymptotic Techniques for Use in Statistics. Chapman and Hall, London.
3. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. 2nd edition. Springer-Verlag, New York.
4. Bhattacharya, R. N. and Rao, R. R. (1976). Normal Approximation And Asymptotic Expansions. Wiley, New York.
5. Brown, L. D. (1986). Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory. Lecture Notes-Monograph Series, Institute of Mathematical Statistics, Hayward, California.
6. Brown, L. D., Cai, T. and DasGupta, A. (2001). Interval estimation for a binomial proportion (with discussion). Statist. Sci. 16, 101-133.
7. Brown, L. D., Cai, T. and DasGupta, A. (2002). Confidence intervals for a binomial proportion and Edgeworth expansions. Ann. Statist. 30, in press.
8. Brown, L. D., Cai, T. and DasGupta, A. (2000). Interval estimation in exponential families. Technical Report, Department of Statistics, University of Pennsylvania.
9. Casella, G. and Robert, C. (1989). Refining Poisson confidence intervals. Canad. J. Statist. 17, 45-57.
10. Clevenson, M. and Zidek, J. (1975). Simultaneous estimation of the means of independent Poisson laws, J. Amer. Stat. Assoc. 70, 698-705.
11. Crow, E. L. and Gardner, R. S. (1959). Confidence intervals for the expectation of a Poisson variable. Biometrika 46, 441-453.
12. Esseen, C. G. (1945). Fourier analysis of distribution functions: a mathematical study of the Laplace-Gaussian law. Acta Math. 77, 1-125.
13. Ghosh, J. K. (1994). Higher Order Asymptotics. NSF-CBMS Regional Conference Series, Institute of Mathematical Statistics, Hayward.
14. Hall, P. (1992). The Bootstrap And Edgeworth Expansion. Springer-Verlag, New York.
15. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions. Second edition, Vol. 2. Wiley, New York.
16. Johnson, R. A. (1970). Asymptotic expansions associated with posterior distributions. Ann. Math. Statist. 41, 851-64.
17. Kaplan, S. (1983). On a "two stage" Bayesian procedure for determining failure rates from experimental data, IEEE Trans. on Power App. and Sys. 102, 195-202.
18. Kabaila, P. and Byrne, J. (2001). Exact short Poisson confidence intervals. Canad. J. Statist. 29, 99-106.
19. Lui, K.-J. (1995). Confidence limits for the population prevalence rate based on the negative binomial distribution. Statist. Medicine 14, 1471-1477.
20. Morris, C. N. (1982). Natural exponential families with quadratic variance functions. Ann. Statist. 10, 65-80.
21. Morris, C. N. (1983). Natural exponential families with quadratic variance functions: statistical theory, Ann. Statist. 11, 515-529.
22. Rao, C. R. (1973). Linear Statistical Inference and Its Applications. Wiley, New York.
23. Santner, T. J. and Duffy, D. E. (1989). The Statistical Analysis of Discrete Data. Springer-Verlag, Berlin.
24. Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.