Limit laws for exponential families

Bernoulli

Volumn 5, Issue 6, 1999, Pages 951-968

  Balkema, August A ^a   Klüppelberg, Claudia ^b   Resnick, Sidney I ^c  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c School of Operations Research and Industrial Engineering   (United States)

Author keywords

Affine transformation; Asymptotic normality; Convergence of types; Cumulant generating function; Esscher transform; Exponential family; Gamma distribution; Gaussian tail; Limit law; Normal distribution

Indexed keywords

EID: 0042408320     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318554     Document Type: Article

References (25)

1. Balkema, A.A., Klüppelberg, C. and Resnick, S.I. (1993) Densities with Gaussian tails. Proc. London Math. Soc. (3), 66, 568-588.
2. Balkema, A.A., Klüppelberg, C. and Stadtmüller, U. (1995) Tauberian results for densities with Gaussian tails. J. London Math. Soc. (2), 51, 383-400.
3. Bar-Lev, S.K. and Casalis, M. (1994) Les familles exponentielles naturelles reproduisantes. C. R. Acad. Sei. Paris, 319, 1323-1326
4. Bar-Lev, S.K. and Casalis, M. (1998) A general property of reproducibility. Ann. Probab. Submitted.
5. Bamdorff-Nielsen, O.E. (1978) Information and Exponential Families in Statistical Tlieory. Chichester: Wiley.
6. Barndorff-Nielsen, O.E. and Cox, D.R. (1994) Inference and Asymptotics. London: Chapman & Hall.
7. Barndorff-Nielsen, O.E. and Klüppelberg, C. (1999) Tail exactness of multivariate saddlepoint approximations. Scand. J. Statist., 26, 1-12.
8. Broniatowski, M. and Mason, D. (1994) Extended large deviations. J. Tfieoret. Probab., 7, 647-666.
9. Brown, L. (1986) Fundamentals of statistical exponential families. IMS Lecture Notes Monogr. Sen, Vol. 9. Hayward, CA: Institute of Mathematical Statistics.
10. Casalis, M. (1991) Familles exponentielles naturelles sur Rd invariantes par un groupe. Internat. Statist. Rev., 59, 241-262.
11. Davis, R. and Resnick, S.I. (1991) Extremes of moving averages of rv's with finite endpoint. Ann. Probab., 19, 312-328.
12. de Haan, L. (1970) On Regular Variation and Its Application to Weak Convergence of Sample Extremes, CWI Tract 32. Amsterdam: Centrum voor Wiskunde en Informatica.
13. de Haan, L. and Resnick, S.I. (1984) Asymptotically balanced functions and stochastic compactness of sample extremes. Ann. Probab., 12, 588-608.
14. Doeblin, W. (1946) Sur l'ensemble de puissances d'une loi de probabilité. Ann. Ecole Normale Supérieure (III), 63, 317-350.
15. Feigin, P. and Yashchin, E. (1983) On a strong Tauberian resuit. Z Watescheinlichkeitstheorie Verw. Geb., 65, 35-48.
16. Feller, W. (1966) An Introduction to Probability Theory, Vol. 2. New York: Wiley.
17. Feller, W. (1969) Limit theorems for probabilities of large deviations. Z. Wahrscheinlichkeitstheorie Venv. Geb. 14, 1-20.
18. Hazod, W. and Scheffler, H.P. (1993) The domains of partial attraction of probabilities on groups and on vector spaces. J. Ttieoret. .Probab., 6, 175-186.
19. Jensen, J.L. (1995) Saddlepoint Approximations. Oxford: Oxford University Press.
20. Lehmann, E.L. (1983) Tlieory of Point Estimation. New York: Wiley.
21. Pancheva, E. (1985) Limit theorems for extreme order statistics under non-linear normalization. In VV. Kalashnikov and V.M. Zolotarev (eds), Stability Problems for-Stochastic Models, Lecture Notes in Math. 1155, pp. 284-309. Berlin: Springer-Verlag.
22. Parthasarathy, K.R. (1967) Probability Measures on Metric Spaces. New York: Academic Press.
23. Ravi S. (1991) Tail equivalence of df's belonging to the max domains of attraction of univariate p-max stable laws. J. Indian Statist. Assoc., 29, 69-77.
24. Rootzen, H. (1987) A ratio limit theorem for the tails of weighted sums. Ann. Probab., 15, 728-747.
25. Teicher, H. (1984) The CLT for Esscher transformed rv's. Sankhyà Ser. A, 46, 35-40.