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
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.
@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},
publisher = {mathdoc},
volume = {25},
number = {4},
year = {1980},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a5/}
}
TY - JOUR AU - D. M. Čibisov TI - Asymptotic expansion for the distribution of a~statistic admitting a~stochastic expansion.~I JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1980 SP - 745 EP - 756 VL - 25 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a5/ LA - ru ID - TVP_1980_25_4_a5 ER -
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/