More General Central Limit Theorems

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)


Central Limit Theorem Stable Distribution Divisible Distribution Large Sample Theory Exchangeable Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aldous, D. (1983). Exchangeability and Related Topics, Lecture Notes in Mathematics, Vol. 1117, Springer, Berlin.Google Scholar
  2. Anscombe, F. (1952). Large sample theory of sequential estimation, Proc. Cambridge Philos. Soc., 48, 600–607.zbMATHMathSciNetCrossRefGoogle Scholar
  3. Billingsley, P. (1995). Probability and Measure, 3rd ed., John Wiley, New York.zbMATHGoogle Scholar
  4. Blum, J., Chernoff, H., Rosenblatt, M., and Teicher, H. (1958). Central limit theorems for interchangeable processes, Can. J. Math., 10, 222–229.zbMATHMathSciNetGoogle Scholar
  5. Bose, A., DasGupta, A., and Rubin, H. (2004). A contemporary review of infinitely divisible distributions and processes, Sankhya Ser. A, 64(3), Part 2, 763–819.Google Scholar
  6. Chernoff, H. and Teicher, H. (1958). A central limit theorem for sums of interchangeable random variables, Ann. Math. Stat., 29, 118–130.CrossRefMathSciNetzbMATHGoogle Scholar
  7. de Finetti, B. (1931). Funzione caratteristica di un fenomeno allatorio. Atti R. Accad. Naz. Lincii Ser. 6, Mem., Cl. Sci. Fis. Mat. Nat., 4, 251–299.Google Scholar
  8. Diaconis, P. (1988). Recent Progress on de Finetti’s Notions of Exchangeability, Bayesian Statistics, Vol. 3, Oxford University Press, New York.Google Scholar
  9. Diaconis, P. and Freedman, D. (1987). A dozen de Finetti style results in search of a theory, Ann. Inst. Henri. Poincaré Prob. Stat., 23(2), 397–423.MathSciNetGoogle Scholar
  10. Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley, New York.zbMATHGoogle Scholar
  11. Ferguson, T. (1996). A Course in Large Sample Theory, Chapman and Hall, London.zbMATHGoogle Scholar
  12. Fisz, M. (1962). Infinitely divisible distributions: recent results and applications, Ann. Math. Stat., 33, 68–84.CrossRefMathSciNetzbMATHGoogle Scholar
  13. Hewitt, E. and Savage, L. (1955). Symmetric measures on Cartesian products, Trans. Am. Math. Soc., 80, 470–501.zbMATHCrossRefMathSciNetGoogle Scholar
  14. Hoeffding, W. (1951). A combinatorial central limit theorem, Ann. Math. Stat., 22, 558–566.CrossRefMathSciNetzbMATHGoogle Scholar
  15. Klass, M. and Teicher, H. (1987). The central limit theorem for exchangeable random variables without moments, Ann. Prob., 15, 138–153.zbMATHCrossRefMathSciNetGoogle Scholar
  16. Lehmann, E.L. (1999). Elements of Large Sample Theory, Springer, New York.zbMATHGoogle Scholar
  17. Lévy, P. (1937). Théorie de ĺ Addition des Variables Aléatoires, Gauthier-Villars, Paris.Google Scholar
  18. Petrov, V. (1975). Limit Theorems for Sums of Independent Random Variables (translation from Russian), Springer-Verlag, New York.Google Scholar
  19. Port, S. (1994). Theoretical Probability for Applications, John Wiley, New York.zbMATHGoogle Scholar
  20. Rényi, A. (1957). On the asymptotic distribution of the sum of a random number of independent random variables, Acta Math. Hung., 8, 193–199.zbMATHCrossRefGoogle Scholar
  21. Sen, P.K. and Singer, J. (1993). Large Sample Methods in Statistics: An Introduction with Applications, Chapman and Hall, New York.zbMATHGoogle Scholar
  22. Steutel, F.W. (1979). Infinite divisibility in theory and practice, Scand. J. Stat., 6, 57–64.CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anirban DasGupta
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

Personalised recommendations