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

Samir Benaissa. "Bernstein inequality for the parameter of the pth order autoregressive process AR(p)." Applicationes Mathematicae 33.3-4 (2006): 253-264. <http://eudml.org/doc/279705>.

@article{SamirBenaissa2006,
abstract = {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.},
author = {Samir Benaissa},
journal = {Applicationes Mathematicae},
keywords = {autoregressive process; exponential inequalities; linear process; limiting distribution},
language = {eng},
number = {3-4},
pages = {253-264},
title = {Bernstein inequality for the parameter of the pth order autoregressive process AR(p)},
url = {http://eudml.org/doc/279705},
volume = {33},
year = {2006},
}

TY - JOUR
AU - Samir Benaissa
TI - Bernstein inequality for the parameter of the pth order autoregressive process AR(p)
JO - Applicationes Mathematicae
PY - 2006
VL - 33
IS - 3-4
SP - 253
EP - 264
AB - 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.
LA - eng
KW - autoregressive process; exponential inequalities; linear process; limiting distribution
UR - http://eudml.org/doc/279705
ER -