×
Niki, Naoto; Konishi, Sadanori

Effects of transformations in higher order asymptotic expansions. (English) Zbl 0609.62075

Ann. Inst. Stat. Math. 38, 371-383 (1986).
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.

Cited in 1 Review
Cited in 13 Documents

MSC:

62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics

Keywords:

Hermite polynomials; Approximate formulae; Edgeworth type asymptotic expansions; tails; oscillations

Software:

REDUCE
PDF BibTeX XML Cite
\textit{N. Niki} and \textit{S. Konishi}, Ann. Inst. Stat. Math. 38, 371--383 (1986; Zbl 0609.62075)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Bhattacharya, R. N.; Ghosh, J. K., On the validity of the formal Edge-worth expansion, Ann. Statist., 6, 434-451, (1978) · Zbl 0396.62010
[2] Fisher, R. A., On the probable error of a coefficient of correlation deduced from a small sample, Metron, 1, 1-32, (1921)
[3] Konishi, S., An approximation to the distribution of the sample correlation coefficient, Biometrika, 65, 654-656, (1978) · Zbl 0391.62037
[4] Konishi, S., Normalizing transformations of some statistics in multivariate analysis, Biometrika, 68, 647-651, (1981) · Zbl 0482.62040
[5] Hearn, A. C. (ed.) (1984).REDUCE User’s Manual, Version 3.1, the Rand Corporation, Santa Monica.
[6] Muirhead, R. J. (1982).Aspects of Multivariate Statistical Theory, Wiley, New York. · Zbl 0556.62028
[7] Niki, N. (1986). Formulae in higher order asymptotic expansions for distributions of statistics, (to appear). · Zbl 0655.62017
[8] Niki, N.; Konishi, S., Higher order asymptotic expansions for the distribution of the sample correlation coefficient, Commun. Statist.-Simula. Computa., 13, 169-182, (1984) · Zbl 0555.62020
[9] Petrov, V. V. (1975).Sums of Independent Random Variables, Springer-Verlag, Berlin. · Zbl 0322.60042
[10] Rao, C. R. (1973).Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York. · Zbl 0256.62002
[11] Siotani, M., Hayakawa, T. and Fujikoshi, Y. (1985).Modern Multivariate Statistical Analysis, American Sciences Press, Ohio. · Zbl 0588.62068
[12] Wallace, D. L., Asymptotic approximations to distributions, Ann. Math. Statist., 29, 635-654, (1958) · Zbl 0086.34004
[13] Wilson, E. B.; Hilferty, M. M., The distribution of chi-square, Proc. Nat. Acad. Sci., 17, 684-688, (1931) · JFM 57.0632.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.