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

100%
Benaissa S.
Applicationes Mathematicae
|
2006
|
tom 33
|
nr 3-4
253-264
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.
2
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Mean square error of the estimator of the conditional hazard function

51%
Rabhi A., Benaissa S., Hamel E. H., Mechab B.
Applicationes Mathematicae
|
2013
|
tom 40
|
nr 4
405-420
EN
This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.
3
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Asymptotic normality of the kernel estimate for the Markovian transition operator

51%
Benaissa S., Rabhi A., Mechab B.
Applicationes Mathematicae
|
2011
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tom 38
|
nr 1
93-105
EN
We build a kernel estimator of the Markovian transition operator as an endomorphism on L¹ for some discrete time continuous states Markov processes which satisfy certain additional regularity conditions. The main result deals with the asymptotic normality of the kernel estimator constructed.
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