Geodesic
The invariance principle for~conditional empirical processes
Izvestiya. Mathematics , Tome 69 (2005) no. 4, pp. 771-789.

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We prove the convergence of finite-dimensional distributions and establish density for Nadaraya–Watson conditional empirical processes. The observations are assumed to be described by a strictly stationary sequence of random variables whose mixing coefficients decay polynomially. The proof of density of such processes in the space of continuous functionals uses entropy conditions on the class of indexing functions. 
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D. V. Poryvai. The invariance principle for~conditional empirical processes. Izvestiya. Mathematics , Tome 69 (2005) no. 4, pp. 771-789. http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a5/

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