Geodesic
More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 369-373

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Let $X_1,X_2,\dots$ be a stationary sequence of $m$-dependent random variables and let $\Phi(x_1,\dots,x_r)$ be a symmetric function. For the distribution of the $U$-statistics $$ U_n=(C_n^r)^{-1}\sum_{1\le i_1\dots\le n}\Phi(X_{i_1},\dots,X_{i_r}) $$ the rate of convergence to the normal law is investigated. 
@article{TVP_1982_27_2_a20,
     author = {T. L. Malevi\v{c} and {\CYRV}. Abdalimov},
     title = {More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {369--373},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a20/}
}
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T. L. Malevič; В. Abdalimov. More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 369-373. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a20/