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Contributions to Ergodic Theory and Probability pp 53–63Cite as

Some results on convergence rates for weighted averages

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References

  1. R.R. Bahadur and R. Ranga Rao, On Deviations of the Sample Mean, Ann. Math. Statist. 31 (1960) 1015–1027.

    Article  MathSciNet  MATH  Google Scholar 

  2. L.E. Baum and M. Katz, Convergence Rates in the Law of Large Numbers, Trans. Amer. Math. Soc. 120 (1965) 108–123.

    Article  MathSciNet  MATH  Google Scholar 

  3. L.E. Baum, M. Katz, and R.P. Read, Exponential Convergence Rates for the Law of Large Numbers, Trans. Amer. Math. Soc. 102 (1962) 187–199.

    Article  MathSciNet  MATH  Google Scholar 

  4. David Blackwell and J.L. Hodges, Jr., The Probability in the Extreme Tail of a Convolution, Ann. Math. Statist. 30 (1959) 1113–1120.

    Article  MathSciNet  MATH  Google Scholar 

  5. J.R. Blum, D.L. Hanson, and L.H. Koopmans, On the Strong Law of Large Numbers for a Class of Stochastic Processes, Z. Wahrscheinlichkeitstheorie 2 (1963) 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Chernoff, A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations. Ann. Math. Statist. 23 (1952) 493–507.

    Article  MathSciNet  MATH  Google Scholar 

  7. Y.S. Chow, Some Convergence Theorems for Independent Random Variables, Ann. Math. Statist. 37 (1966) 1482–1493.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Cramer, Sur un Nouveau Théorème-Limite de la Theorie des Probabilities, Actualités Sci. Ind., No. 736, Paris (1938).

    Google Scholar 

  9. P. Erdős, On a Theorem of Hsu and Robbins, Ann. Math. Statist. 20 (1949) 286–291.

    Article  MathSciNet  MATH  Google Scholar 

  10. W.E. Franck and D.L. Hanson, Some Results Giving Rates of Convergence in the Law of Large Numbers for Weighted Sums of Independent Random Variables, Trans. Amer. Math. Soc. 124 (1966) 347–359.

    Article  MathSciNet  MATH  Google Scholar 

  11. D.L. Hanson, Some Results Relating Moment Generating Functions and Convergence Rates in the Law of Large Numbers, Ann. Math. Statist. 38 (1967) 742–750.

    Article  MathSciNet  MATH  Google Scholar 

  12. D.L. Hanson and Melvin Katz, On the Oscillation of Sums of Random Variables, Proc. Amer. Math. Soc. 17 (1966) 864–865.

    Article  MathSciNet  MATH  Google Scholar 

  13. D.L. Hanson and L.H. Koopmans, On the Convergence Rate of the Law of Large Numbers for Linear Combinations of Independent Random Variables, Ann. Math. Statist. 36 (1965) 559–564.

    Article  MathSciNet  MATH  Google Scholar 

  14. D.L. Hanson and L.H. Koopmans, Convergence Rates for the Law of Large Numbers for LInear Combinations of Exchangeable and *-Mixing Stochastic Processes, Ann. Math. Statist. 36 (1965) 1840–1852.

    Article  MathSciNet  MATH  Google Scholar 

  15. D.L. Hanson and L.H. Koopmans, A Probability Bound for Integrals With Respect to Stochastic Processes With Independent Increments, Proc. Amer. Math. Soc. 16 (1965) 1173–1177.

    Article  MathSciNet  MATH  Google Scholar 

  16. D.L. Hanson and F.T. Wright, Some More Results on Rates of Convergence in the Law of Large Numbers for Weighted Sums of Independent Random Variables, Tran. Amer. Math. Soc. 141 (1969) 443–464.

    Article  MathSciNet  MATH  Google Scholar 

  17. D.L. Hanson and F.T. Wright, Some Convergence Results for Weighted Sums of Independent Random Variables, Unpublished.

    Google Scholar 

  18. C.C. Heyde and V.K. Rohatgi, A Pair of Complementary Theorems On Convergence Rates in the Law of Large Numbers, Proc. Camb. Phil. Soc. 63 (1967) 73–82.

    Article  MathSciNet  MATH  Google Scholar 

  19. J.J. Higgins, Communication.

    Google Scholar 

  20. P.L. Hsu and H. Robbins, Complete Convergence and the Law of Large Numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947) 25–31.

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Jamison, S. Orey, and W. Pruitt, Convergence of Weighted Averages of Independent Random Variables, Z. Wahrscheinlichkeitstheorie 4 (1965) 40–44.

    Article  MathSciNet  MATH  Google Scholar 

  22. Melvin L. Katz, The Probability in the Tail of a Distribution, Ann. Math. Statist. 34 (1963) 312–318.

    Article  MathSciNet  MATH  Google Scholar 

  23. Melvin L. Katz, Communication.

    Google Scholar 

  24. W.E. Pruitt, Summability of Independent Random Variables, J. Math. Mech. 15 (1966) 769–776.

    MathSciNet  MATH  Google Scholar 

  25. V.K. Rohatgi, On Convergence Rates in the Law of Large Numbers for Weighted Sums of Independent Random Variables, Proc. Amer. Math. Soc. 20 (1969) 570–574.

    Article  MathSciNet  MATH  Google Scholar 

  26. W.F. Stout, Some Results on the Complete and Almost Sure Convergence of Linear Combinations of Independent Random Variables and Martingale Differences, Ann. Math. Statist. 39 (1968) 1549–1562.

    MathSciNet  MATH  Google Scholar 

  27. F.T. Wright, Communication.

    Google Scholar 

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Authors and Affiliations

  1. University of Missouri-Columbia, USA

    D. L. Hanson

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  1. D. L. Hanson
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© 1970 Springer-Verleg

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Hanson, D.L. (1970). Some results on convergence rates for weighted averages. In: Contributions to Ergodic Theory and Probability. Lecture Notes in Mathematics, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060646

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  • DOI: https://doi.org/10.1007/BFb0060646

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05188-6

  • Online ISBN: 978-3-540-36371-2

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