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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:
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In this paper we study the convergence in distribution of the linear operator for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.
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 -