Geodesic
Asymptotic expansion for the distribution of a statistic admitting a stochastic expansion. I
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 745-756 
D. M. Čibisov. Asymptotic expansion for the distribution of a statistic admitting a stochastic expansion. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 745-756. http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a5/
@article{TVP_1980_25_4_a5,
     author = {D. M. \v{C}ibisov},
     title = {Asymptotic expansion for the distribution of a~statistic admitting a~stochastic {expansion.~I}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {745--756},
     year = {1980},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $(Y_{0i},\mathbf Y_i)=(Y_{0i},Y_{1i},\dots,Y_{pi})$, $i=1,\dots,n$, be i.i.d. random vectors in $R^{p+1}$, and $\{h_j\}$ be a finite set of polinomials of $p+1$ variables. Let \begin{gather*} S_n=n^{-1/2}\sum Y_{0i},\qquad T_{nl}=n^{-1/2}\sum Y_{li},\qquad\mathbf T_n=(T_{n1},\dots,T_{np}), \\ Z_n=S_n+\sum n^{-j/2}h_j(S_n,\mathbf T_n). \end{gather*} In the paper an asymptotic expansion of the Edgeworth's type for the distribution function of $Z_n$ is obtained under conditions which are weaker than those previously known.