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A new look at the relationship between Edgeworth expansion and saddlepoint approximation. (English) Zbl 0765.62025

Summary: The Edgeworth expansion of the density of the sample mean is obtained, up to the second order, by expanding the saddlepoint approximation. This is achieved through an expansion of the saddlepoint which gives an explicit formula to the latter approximation.

MSC:

62E20 Asymptotic distribution theory in statistics
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References:

[1] Daniels, H. E., Saddlepoint approximation in statistics, Ann. Math. Statist., 25, 631-650 (1954) · Zbl 0058.35404
[2] Field, C. A.; Hampel, F. R., Small-sample asymptotic distributions for M-estimators of location, Biometrika, 62, 29-46 (1982) · Zbl 0495.62025
[3] Ronchetti, E.; Welsh, A., Empirical small sample asymptotics for Multivariate M-estimators, J. Roy. Statist. Soc. Ser. B. (1991), to appear in
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