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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2005 Volume 69, Issue 4, Pages 129–148 (Mi im650)

This article is cited in 2 papers

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.

UDC: 519.214.5+519.234.22

MSC: 60F17, 62G05

Received: 21.07.2004

DOI: 10.4213/im650


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

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© Steklov Math. Inst. of RAS, 2026