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Effects of transformations in higher order asymptotic expansions

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Summary

Approximate formulae using a large number of terms of Edgeworth type asymptotic expansions for the distributions of statistics often produce spurious oscillations and give poor fits to the exact distribution functions in parts of the tails. A general method for suppressing these oscillations and evoking more accurate approximations is introduced here.

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References

  1. Bhattacharya, R. N. and Ghosh, J. K. (1978). On the validity of the formal Edge-worth expansion,Ann. Statist.,6, 434–451.

    Article  MathSciNet  Google Scholar 

  2. Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample,Metron,1, 1–32.

    Google Scholar 

  3. Konishi, S. (1978). An approximation to the distribution of the sample correlation coefficient,Biometrika,65, 654–656.

    Article  MathSciNet  Google Scholar 

  4. Konishi, S. (1981). Normalizing transformations of some statistics in multivariate analysis,Biometrika,68, 647–651.

    Article  MathSciNet  Google Scholar 

  5. Hearn, A. C. (ed.) (1984).REDUCE User's Manual, Version 3.1, the Rand Corporation, Santa Monica.

    Google Scholar 

  6. Muirhead, R. J. (1982).Aspects of Multivariate Statistical Theory, Wiley, New York.

    Book  Google Scholar 

  7. Niki, N. (1986). Formulae in higher order asymptotic expansions for distributions of statistics, (to appear).

  8. Niki, N. and Konishi, S. (1984). Higher order asymptotic expansions for the distribution of the sample correlation coefficient,Commun. Statist.-Simula. Computa.,B13, 169–182.

    Article  MathSciNet  Google Scholar 

  9. Petrov, V. V. (1975).Sums of Independent Random Variables, Springer-Verlag, Berlin.

    Book  Google Scholar 

  10. Rao, C. R. (1973).Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York.

    Book  Google Scholar 

  11. Siotani, M., Hayakawa, T. and Fujikoshi, Y. (1985).Modern Multivariate Statistical Analysis, American Sciences Press, Ohio.

    MATH  Google Scholar 

  12. Wallace, D. L. (1958). Asymptotic approximations to distributions,Ann. Math. Statist.,29, 635–654.

    Article  MathSciNet  Google Scholar 

  13. Wilson, E. B. and Hilferty, M. M. (1931). The distribution of chi-square,Proc. Nat. Acad. Sci.,17, 684–688.

    Article  Google Scholar 

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Additional information

This work was supported in part by Ministry of Education Grant 59530016 and 60530017.

The Institute of Statistical Mathematics

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Niki, N., Konishi, S. Effects of transformations in higher order asymptotic expansions. Ann Inst Stat Math 38, 371–383 (1986). https://doi.org/10.1007/BF02482524

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  • DOI: https://doi.org/10.1007/BF02482524

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