EXPONENTIAL TYPE INEQUALITIES AND ALMOST COMPLETE CONVERGENCE OF THE OPERATOR ESTIMATOR OF FIRST-ORDER AUTOREGRESSIVE IN HILBERT SPACE GENERATED BY WOD ERROR
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Published:2023-09-30
Issue:3
Volume:23
Page:671-680
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ISSN:2068-3049
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Container-title:Journal of Science and Arts
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language:en
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Short-container-title:J. Sci. Arts
Author:
HAMMAD MALIKA1, BOULENOIR ZOUAOUIA2, BENAISSA SAMIR1
Affiliation:
1. University of DjillaliLiabes, Department of Probability and Statistics, Laboratory of Statistics and Stochastic Processes, 22000 SidiBel Abbes, Algeria. 2. Ecole Supérieure en Informatique 08 Mai 1945, 22000 Sidi Bel Abbes, Algeria.
Abstract
In this paper, we establish a new concentration inequality and almost complete convergence of the value of the process of autoregressive Hilbertian of order one (ARH (1)), which directly stems from works of Serge Guillas, Denis Bosq, that is defined by X_t= ρ(X_(t- 1)) +ζ_t; t∈ Z where the random variables are all Hilbertian, ρ is a linear operator on a space of separable Hilbert and ζ_t which constitute a widely orthant dependent error (WOD, in short) after recalling some results on the finite-dimensional model of this type, we introduce the mathematical and statistical tools which will be used afterwards. Then we build an estimator of the operator and we establish its asymptotic properties.
Publisher
Valahia University of Targoviste - Journal of Science and Arts
Subject
General Earth and Planetary Sciences,General Environmental Science
Reference30 articles.
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