Existence of maximum likelihood estimates for multi-dimensional exponential families

Scandinavian Journal of Statistics

Volumn 24, Issue 3, 1997, Pages 371-386

  Miao, Weiwen ^a   Hahn, Marjorie ^b  

^a MOUNT HOLYOKE COLLEGE   (United States)

^b TUFTS UNIVERSITY   (United States)

Author keywords

Existence; Exponential families; Maximum likelihood

Indexed keywords

EID: 0031521749     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00070     Document Type: Article

References (13)

1. Barndorff-Nielsen, O. (1978). Information and exponential families in statistical theory. Wiley, New York.
2. Berk, R. (1972). Consistency and asymptotic normality of MLE for exponential models. Ann. Statist. 43, 193-204.
3. Brown, L. D. (1986). Fundamentals of Statistical Exponential Families. IMS Lecture Notes - Monograph Series, Vol. 9. Hayward, CA.
4. Dudley, D. & Haughton, D. (1997). Information criteria for multiple data sets and restricted parameters. To appear in Statist. Science, special issue on model selection.
5. Efron, B. (1978). The geometry of exponential families. Ann. Statist. 6, 362-376.
6. Geyer, C. (1990). Likelihood and exponential families. PhD dissertation at University of Washington.
7. Haughton, D. (1988). On the choice of a model to fit data from an exponential family. Ann. Statist. 16, 342-355.
8. Hoffmann-Jørgensen, J. (1994a). Probability with a view towards statistics, vol. I. Chapman & Hall, New York.
9. Hoffmann-Jørgensen, J. (1994b). Probability with a view towards statistics, vol. II. Chapman & Hall, New York.
10. Miao, W. & Hahn, M. (1996). Existence and strong consistency of maximum likelihood estimates for 1-dimensional exponential families. Statist. Probab. Lett. 28, 9-21.
11. Miao, W. (1995). Maximum likelihood estimation for exponential families. PhD dissertation, Tufts University.
12. Pazman, A. (1986). On the uniqueness of the M. L. estimates in curved exponential families. Kybernetika 22, 124-132.
13. Rockafellar, R. T. (1972). Convex analysis. Princeton University Press, Princeton, New Jersey.