Asymptotic probabilities of over-estimating and under-estimating the order of a model in general regular families

Communications in Statistics - Theory and Methods

Volumn 32, Issue 7, 2003, Pages 1373-1404

  Keribin, C ^a   Haughton, D ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b BENTLEY COLLEGE   (United States)

Author keywords

Information criteria; Large deviations; Model selection; Moderate deviations; Negative binomial distributions; Penalized maximum likelihood

Indexed keywords

MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; STATISTICAL TESTS;

BINOMIAL DISTRIBUTIONS;

PROBABILITY DISTRIBUTIONS;

EID: 0037766362     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120021564     Document Type: Article

References (18)

1. Abramowitz, M., Stegun, I. (1970). Handbook of Mathematical Functions, ninth printing. New York: Dover.
2. Akaike, H. (1984). Information theory and an extension of the maximum likelihood principle. Second International Symposium on Information Theory. Petrovm B. N., Czàki, F., eds. Budapest: Akademiai Kiadò, 267-281.
3. Azencott, R. Dacunha-Castelle, D. (1984). Series d'observations irrégulières. Paris: Masson.
4. Brown, L. (1986). Fundamentals of statistical exponential families. Lecture Notes - Monograph Series. Hayward, California: Institute of Mathematical Statistics.
5. Dacunha-Castelle, D., Duflo, M. (1993). Probabilités et statistiques: 2- Problèmes à temps mobile. Paris: Masson.
6. Dembo, A., Zeitouni, O. (1993). Large Deviations Techniques and Applications. Boston: Jones and Bartlett Publishers.
7. Haughton, D. (1988). On the choice of a model to fit data from an exponential family. Annals of Statistics 16:342-355.
8. Haughton, D. (1989). Size of the error in the choice of a model to fit data from an exponential family. Sankhyā A 51:45-58.
9. Leroux, B. G. (1992). Consistent estimation of a mixing distribution. Annals of Statistics 20(3): 1350-1360.
10. Mogulskii, A. A. (1988). Large deviations for maximum likelihood estimators. Lecture Notes in Mathematics 1299:326-331.
11. Nelson, J. (1980). Multiple victimizations in American cities: a statistical analysis of rare events. American Journal of Sociology 85(4):870-891.
12. Nishii, R. (1984). Asymptotic properties of criteria for selection of variables in multiple regression. Annals of Statistics 12:758-765.
13. Ortiz, E. (1990). A stochastic model of the distribution of wars in time: the negative binomial distribution. ASA Proceedings of the Section on Social Statistics, 285-290.
14. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6:461-464.
15. Van der Vaart, A. W., Wellner, J. A. (1996). Weak Convergence and Empirical Processes. Springer Verlag: Springer Series in Statistics.
16. Wilks, S. S. (1967). Mathematical Statistics. New York: Wiley.
17. Woodroofe, M. (1982). On model selection and the generalized arc sine laws. Annals of Statistics 10(4): 1182-1194.
18. Wright, Q. (1970). A Study of War. Chicago: University of Chicago Press.