Edgeworth Expansions and Smoothness
Bickel, P. J. ; Robinson, J.
Ann. Probab., Tome 10 (1982) no. 4, p. 500-503 / Harvested from Project Euclid
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We give a necessary and sufficient condition for the distribution function of $n^{-1/2} \sum^n_{i=1} X_i$, where the $X_i$ are independently identically distributed with $EX_1 = 0, EX^2_1 = 1$ and $E|X_1|^{k+3} < \infty$, to possess an Edgeworth expansion to $k$ terms. The condition is not practicable but clarifies the relation between the existence of an Edgeworth expansion and the smoothness of the distribution function of the sum.
Publié le : 1982-05-14
Classification:  Edgeworth expansions,  central limit theorem,  60F05 
@article{1176993873,
     author = {Bickel, P. J. and Robinson, J.},
     title = {Edgeworth Expansions and Smoothness},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 500-503},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993873}
}

Bickel, P. J.; Robinson, J. Edgeworth Expansions and Smoothness. Ann. Probab., Tome 10 (1982) no. 4, pp.  500-503. http://gdmltest.u-ga.fr/item/1176993873/