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Helmut Finner  -  DDZ  -  Institut fŁr Biometrie und Epidemiologie  -  Auf'm Hennekamp 65  -  D-40225 Duesseldorf


Edgeworth expansions for Student's t-statistic

Three Maple worksheets are availble for the computation
of higher order Edgeworth expansions for Student's t-statistic

1)  
Finner-Dickhaus-Chung.mws

       Computation based on Chung (1946)

2) 
Finner-Dickhaus-Bartlett-Gayen.mws

      Computation based on Bartlett (1935) and Gayen (1949)


3) 
Finner-Dickhaus-Hall.mws

      Computation based on a smooth function approach described in Hall (1992)


PDF files of these Maple Worksheets with output are also available:

1)  
Finner-Dickhaus-Chung.pdf

2)  
Finner-Dickhaus-Bartlett-Gayen.pdf

3)  
Finner-Dickhaus-Hall.pdf


References:

Finner, H., Dickhaus, T. (2010). Edgeworth expansions and rates of convergence for
normalized sums: Chung's 1946 method revisited.
Statistics and Probability Letters 80(23-24), 1875-1880.

Bartlett, M. S. (1935). The effect of non-normality on the t distribution. Proc. Camb.
Philos. Soc. 31, 223-231.
Chung, K.-L. (1946). The approximate distribution of Studentís statistics. Ann.
Math. Stat. 17, 447-465.
Gayen, A. K. (1949). The distribution of ĎStudentísí t in random samples of any size
drawn from non-normal universes. Biometrika 36, 353-369.
Hall, P. (1987). Edgeworth expansion for Studentís t statistic under minimal moment
conditions. Ann. Prob. 15, 920-931.
Hall, P. (1992). The bootstrap and Edgeworth expansion. Springer Series in Statistics,
New York.
Hsu, P. L. (1945). The approximate distributions of the mean and variance of a
sample of independent variables. Ann. Math. Stat. 16, 1-29.
Wallace, D. L. (1958). Asymptotic approximations to distributions.
Ann. Math. Stat.
29, 635-654.

     


INSTITUTE OF BIOMETRICS AND EPIDEMIOLOGY | GERMAN DIABETES CENTER | UNIVERSITY OF DUESSELDORF