Geodesic
The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables
Sbornik. Mathematics, Tome 27 (1975) no. 4, pp. 554-563

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In this paper the notion of homogeneous vector-valued $U$-statistic is introduced and a central limit theorem is proved for such statistics of a sequence of finitely dependent random variables, which generalizes analogous results for ordinary $U$-statistics. The convergence of finite-dimensional distributions of some random processes generated by $U$-statistics is also studied. Bibliography: 5 titles. 
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     author = {V. G. Mikhailov},
     title = {The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables},
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V. G. Mikhailov. The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables. Sbornik. Mathematics, Tome 27 (1975) no. 4, pp. 554-563. http://geodesic.mathdoc.fr/item/SM_1975_27_4_a6/