Bernstein inequality for the parameter of the pth order autoregressive process AR(p)

• Autorzy: Samir Benaissa
• Języki publikacji: EN

Abstrakty

EN

The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter θ̃ of the first-order autoregressive process taking values in a real separable Banach space B (ARB(1)), if it satisfies the following relation:
$X̃_t = θ̃ X̃_{t-1} + ε̃_t$.
In this paper we study the convergence in distribution of the linear operator $I(θ̃_T, θ̃)= (θ̃_T-θ̃)θ̃^{T-2}$ for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.

Kategorie tematyczne

• 60G25: Prediction theory
• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 60F15: Strong theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2006
• Tom: 33
• Numer: 3-4
• Strony: 253-264

Daty

wydano

2006

Twórcy

autor

Samir Benaissa

• Laboratoire de Mathématiques, Université Djillali Liabès, B.P. 89, Sidi Bel Abbès 22000, Algeria

Identyfikatory

DOI

10.4064/am33-3-1