Bernstein inequality for the parameter of the pth order autoregressive process AR(p)
Samir Benaissa
Applicationes Mathematicae, Tome 33 (2006), p. 253-264 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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: X̃t=θ̃X̃t-1+ε̃t. In this paper we study the convergence in distribution of the linear operator I(θ̃T,θ̃)=(θ̃T-θ̃)θ̃T-2 for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:279705 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am33-3-1,
     author = {Samir Benaissa},
     title = {Bernstein inequality for the parameter of the pth order autoregressive process AR(p)},
     journal = {Applicationes Mathematicae},
     volume = {33},
     year = {2006},
     pages = {253-264},
     zbl = {1107.62083},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am33-3-1}
}

Samir Benaissa. Bernstein inequality for the parameter of the pth order autoregressive process AR(p). Applicationes Mathematicae, Tome 33 (2006) pp. 253-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am33-3-1/