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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 4, Pages 129–148 (Mi izv650)  

The invariance principle for conditional empirical processes formed by dependent random variables

D. V. Poryvai

M. V. Lomonosov Moscow State University

Abstract: 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.

DOI: https://doi.org/10.4213/im650

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English version:
Izvestiya: Mathematics, 2005, 69:4, 771–789

Bibliographic databases:

UDC: 519.214.5+519.234.22
MSC: 60F17, 62G05
Received: 21.07.2004

Citation: D. V. Poryvai, “The invariance principle for conditional empirical processes formed by dependent random variables”, Izv. RAN. Ser. Mat., 69:4 (2005), 129–148; Izv. Math., 69:4 (2005), 771–789

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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