EXPONENTIAL TYPE INEQUALITIES AND ALMOST COMPLETE CONVERGENCE OF THE OPERATOR ESTIMATOR OF FIRST-ORDER AUTOREGRESSIVE IN HILBERT SPACE GENERATED BY WOD ERROR

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.