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Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

100%
Bouchentouf A., Djebbouri T., Rabhi A., Sabri K.
Applicationes Mathematicae
|
2014
|
tom 41
|
nr 4
301-322
EN
The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimator of this model. Asymptotic properties are stated for each of these estimators, and they are applied to the estimation of the conditional mode and conditional quantiles.
2
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Mean square error of the estimator of the conditional hazard function

100%
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

100%
Benaissa S., Rabhi A., Mechab B.
Applicationes Mathematicae
|
2011
|
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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