Advertisement

Measurement Techniques

, Volume 50, Issue 2, pp 132–141 | Cite as

The power of goodness of fit tests for close alternatives

  • B. Yu. Lemeshko
  • S. B. Lemeshko
  • S. N. Postovalov
Article

Abstract

The power of a number of goodness of fit tests when checking simple and complex hypotheses is analyzed by statistical modeling methods. Estimates are given of the power of the tests when checking hypotheses of certain relatively close alternatives. The results enable the tests to be arranged in order of power.

Key words

goodness of fit power Kolmogorov Cramer-von Mises-Smirnov Anderson-Darling Pearson, and Rao-Robson-Nikulin goodness of fit tests 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. N. Bol’shev and N. V. Smirnov, Tables of Mathematical Statistics [in Russian], Nauka, Moscow (1983).zbMATHGoogle Scholar
  2. 2.
    L. N. Bol’shev, Teor. Veroyat. Primenen., 8, No. 2, 129 (1963).Google Scholar
  3. 3.
    M. Kac, J. Kiefer, and J. Wolfowitz, Ann. Math. Stat., 26, 189 (1955).MathSciNetGoogle Scholar
  4. 4.
    R 50.1.037-2002, Recommendations on Standardization. Applied Statistics. Rules for Checking the Goodness of Fit of an Experimental Distribution with Theoretical Ones. Pt. II. Nonparametric Test [in Russian], Izd. Standartov, Moscow (2002).Google Scholar
  5. 5.
    B. Yu. Lemeshko and S. N. Postovalov, Zavod. Lab., 64, No. 3, 61 (1998).Google Scholar
  6. 6.
    B. Yu. Lemeshko and S. N. Postovalov, Zavod. Lab., 67, No. 7, 62 (2001).Google Scholar
  7. 7.
    B. Yu. Lemeshko and S. N. Postovalov, Avtometr., No. 2, 88 (2001).Google Scholar
  8. 8.
    B. Yu. Lemeshko and A. A. Maklakov, Avtometr., No. 3, 3 (2004).Google Scholar
  9. 9.
    G. Cramer, Mathematical Methods of Statistics [Russian translation], Mir, Moscow (1975).Google Scholar
  10. 10.
    B. Yu. Lemeshko and E. V. Chimitova, Zavod. Lab. Diagnostika, Materialov, 70, No. 1, 54 (2004).Google Scholar
  11. 11.
    R 50.1.033-2001, Recommendations on Standardization. Applied Statistics. Rules for Checking the Goodness of Fit of an Experimental Distribution with Theoretical Ones. Pt. I. Chi-Squared Type Tests [in Russian], Izd. Standartov, Moscow (2002).Google Scholar
  12. 12.
    B. Yu. Lemeshko, Zavod. Lab., 64, No. 1, 56 (1998).Google Scholar
  13. 13.
    A. W. Van der Vaart, Asymptotic Statistics, University Press, Cambridge (1998).zbMATHGoogle Scholar
  14. 14.
    M. S. Nikulin, Teor. Veroyat. Primeneniya, XVIII, No. 3, 675 (1973).Google Scholar
  15. 15.
    M. Mirvaliev and M. S. Nikulin, Zavod. Lab., 58No. 3, 52 (1992).Google Scholar
  16. 16.
    P. E. Greenwood and M. S. Nikulin, A Guide to Chi-Squared Testing, John Wiley, New York (1996).zbMATHGoogle Scholar
  17. 17.
    B. Yu. Lemeshko and E. V. Chimitova, Zavod. Lab. Diagnostika Materialov, 69, No. 1, 61 (2003).Google Scholar
  18. 18.
    B. Yu. Lemeshko and S. B. Lemeshko, Metrologiya, No. 2, 3 (2005).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • B. Yu. Lemeshko
    • 1
  • S. B. Lemeshko
    • 1
  • S. N. Postovalov
    • 1
  1. 1.Novosibirsk State Technical UniversityNovosibirsk

Personalised recommendations