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An Asymptotic Expansion for Distributions of C(α) Test Statistics

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Mathematical Statistics and Probability Theory

Part of the book series: Lecture Notes in Statistics ((LNS,volume 2))

Abstract

In the paper an asymptotic expansion (a.e.) for distribution functions (d.f’s) of Neyman’s C(α) test statistics to order n−1/2 (with a remainder 0(n−1/2) is obtained under weaker conditions than previously known (Theorem 2.2). The proof is based on a special theorem giving an a.e.for the d.f. of a statistic admitting a stochastic expansion (Theorem 2.1).

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References

  1. Bikja1is, A., Asymptotic expansions for the densities and distributions of sums of independent identically distributed random vectors. Litovsk. Mat. Sb., 8, 405–422 (1968) =Selected Transi. in Math. Statist. and Probability, 13, 213–234 (1973).

    Google Scholar 

  2. Chibisov, D. M., On the normal approximation for a certain class of statistics. Proc. 6th Berkeley Sympos.Math. Statist, and Prob., vol. 1, 153–174 (1972).

    MathSciNet  Google Scholar 

  3. Chibisov, D. M., Asymptotic expansions for distributions of some test statistics for composite hypotheses. Teor. Ver. i Primen., 17, 3, 600–602 (1972).

    Google Scholar 

  4. Chibisov, D. M., An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion. Teor. Ver. i Primen., 17,4, 658–668 = Theor. Probability Appl., 17, 620–630 (1972).

    Google Scholar 

  5. Chibisov, D. M., Asymptotic expansions for Neyman’s C(oc) tests. Proc. 2nd Japan-USSR Sympos. on Prob. Theory (G. Maruyama and Yu.V.Prokhorov, eds.). Lecture Notes in Math., No. 330, Springer,Berlin, 16–45 (1973).

    Google Scholar 

  6. Chibisov, D. M., An asymptotic expansion for distributionsof sums of a special form with an application to minimum contrast estimates. Teor. Ver. i Primen., 18, 4, 689–702 = Theor. Probability Appl., 18, 649–661 (1973).

    MATH  Google Scholar 

  7. Chibisov, D. M., Weakening the regularity conditions for some asymptotic expansions. Asymptotic Methods in Statistics,10.11–16.11.1974, Tagungsbericht N 44, Mathematisches Forschungsinstitut Oberwolfach, 6–7 (1974).

    Google Scholar 

  8. Chibisov, D. M., On an asymptotic expansion for the distribution of a statistic admitting a stochastic expansion. Teor. Ver. i Primen., 24, 1, 230–231 (1979).

    MathSciNet  Google Scholar 

  9. Chibisov, D. M., Asymptotic expansion for the distribution of statistic admitting a stochastic expansion. Preprints in Statistics, 47, University of Cologne (1979).

    Google Scholar 

  10. Eliseev, V. G.,Asymptotic expansions under local alternatives. Teor. Ver. i Primen., 24, 1, 231–232 (1979).

    Google Scholar 

  11. Fe11er, W., An Introduction to Probability Theory and Its Applications. Vol. II. Wiley, New York 1966.

    MATH  Google Scholar 

  12. Fuc, D. H. and Nagaev, S. V., Probability inequalities for sums of independent random variables. Teor. Ver. i Primen., 10, 4, 660–675 (1971).

    Google Scholar 

  13. Lehmann, E. L. Testing Statistical Hypotheses.Wiley, New York 1959.

    MATH  Google Scholar 

  14. Loéve, M., Probability Theory. Princeton,van Nostrand 1960.

    Google Scholar 

  15. Neyman, J., Optimal asymptotic tests of composite statistical hypotheses.Probability and Statistics (The Harald Cramer Volume). Uppsala, Almquist and Wiksells, 213–234 (1959).

    Google Scholar 

  16. Pfanzag1, J.,Asymptotically optimum estimation and test procedures. Proc. Prague Sympos. on Asymptotic Statistics 3–6 September 1973, Prague, vol. I, 201–272 (1974).

    Google Scholar 

  17. Pfanzag1, J. and Wefe1meyer, W., An asymptotically complete class of tests. Z. Wahrscheinlichkeitstheorie and Verw. Gebiete, 45, 49–72 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  18. Zo1otarev, V. M.,Estimates for differences of distributions in Levy metric, Trudy of Steklov Math. Inst., 112, 224–231 (1971).

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    Dimitr M. Chibisov

Authors
  1. Dimitr M. Chibisov
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Editor information

Editors and Affiliations

  1. Mathematical Institute of the Polish Academy of Science, Kopernika 18, 51-617, Wrocław, Poland

    Witold Klonecki , Andrzej Kozek  & Jan Rosiński ,  & 

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© 1980 Springer-Verlag New York Inc.

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Chibisov, D.M. (1980). An Asymptotic Expansion for Distributions of C(α) Test Statistics. In: Klonecki, W., Kozek, A., Rosiński, J. (eds) Mathematical Statistics and Probability Theory. Lecture Notes in Statistics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7397-5_5

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  • DOI: https://doi.org/10.1007/978-1-4615-7397-5_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90493-1

  • Online ISBN: 978-1-4615-7397-5

  • eBook Packages: Springer Book Archive

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