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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
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