More General Weak and Strong Laws and the Delta Theorem

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


Ergodic Theorem Iterate Logarithm Multivariate Normal Distribution General Weak Large Sample Theory 
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  1. Bickel, P. and Doksum, K. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  2. Birkhoff, G. (1931). Proof of the Ergodic theorem, Proc. Nat. Acad. Sci. USA, 17, 656–660.MATHCrossRefGoogle Scholar
  3. Breiman, L. (1968). Probability, Addison-Wesley, New York.MATHGoogle Scholar
  4. Chung, K.L. (2001). A Course in Probability Theory, 3rd ed., Academic Press, San Diego, CA.Google Scholar
  5. Chung, K.L. and Fuchs, W. (1951). On the distribution of values of sums of random variables, Memoir 6, American Mathematical Society, Providence, RI.Google Scholar
  6. Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Vols. I, II, John Wiley, New York.Google Scholar
  7. Ferguson, T. (1996). A Course in Large Sample Theory, Chapman and Hall, London.MATHGoogle Scholar
  8. Kesten, H. (1972). Sums of independent random variables—without moment conditions, the 1971 Rietz Lecture, Ann. Math. Stat., 43, 701–732.CrossRefMathSciNetGoogle Scholar
  9. Lehmann, E.L. (1999). Elements of Large Sample Theory, Springer, New York.MATHGoogle Scholar
  10. Maller, R. (1980). A note on domains of partial attraction, Ann. Prob., 8, 576–583.MATHCrossRefMathSciNetGoogle Scholar
  11. Revesz, P. (1968). The Laws of Large Numbers, Academic Press, New York.MATHGoogle Scholar
  12. Schneider, I. (1987). The Intellectual and Mathematical Background of the Law of Large Numbers and the Central Limit Theorem in the 18th and the 19th Centuries, Cahiers Histoire et de Philosophie des Sciences Nowlle Serie Societe Francaise d’ Histoire des Sciences et des Techniques, Paris.Google Scholar
  13. Sen, P.K. and Singer, J. (1993). Large Sample Methods in Statistics: An Introduction with Applications, Chapman and Hall, New York.MATHGoogle Scholar
  14. Serfling, R. (1980). Approximation Theorems of Mathematical Statistics, John Wiley, New York.MATHGoogle Scholar
  15. Strassen, V. (1964). An invariance principle for the law of the iterated logarithm, Z. Wahr. Verw. Geb., 3, 211–226.MATHCrossRefMathSciNetGoogle Scholar
  16. Strassen, V. (1966). A converse to the law of the iterated logarithm, Z. Wahr. Verw. Geb., 4, 265–268.MATHCrossRefMathSciNetGoogle Scholar
  17. Tong, Y. (1990). The Multivariate Normal Distribution, Springer-Verlag, New York.MATHGoogle Scholar
  18. van der Vaart, A. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge.MATHGoogle Scholar

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

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

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