The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Ali Laksaci - One of the best experts on this subject based on the ideXlab platform.
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A recursive Kernel Estimate of the functional modal regression under ergodic dependence condition
Journal of statistical theory and practice, 2016Co-Authors: Fatima Zohra Ardjoun, Larbi Ait Hennani, Ali LaksaciAbstract:In this article, we consider an alternative estimator of the conditional mode when the explanatory variable takes values in a semimetric space. This alternative Estimate is based in a recursive Kernel method. Under the ergodicity hypothesis, we quantify the asymptotic properties of this Estimate, by giving the almost complete convergence rate. The asymptotic normality of this Estimate is also given. Our approach is illustrated by a real data application.
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Recursive Kernel Estimate of the conditional quantile for functional ergodic data
Communications in Statistics - Theory and Methods, 2015Co-Authors: Fatima Benziadi, Ali Laksaci, Fethallah TebbouneAbstract:ABSTRACTIn this article, we study the recursive Kernel estimator of the conditional quantile of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. Two estimators are considered. While the first one is given by inverting the double-Kernel Estimate of the conditional distribution function, the second estimator is obtained by using the robust approach. We establish the almost complete consistency of these Estimates when the observations are sampled from a functional ergodic process. Finally, a simulation study is carried out to illustrate the finite sample performance of these estimators.
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asymptotic properties of the Kernel Estimate of spatial conditional mode when the regressor is functional
AStA Advances in Statistical Analysis, 2015Co-Authors: Sophie Daboniang, Zoulikha Kaid, Ali LaksaciAbstract:The Kernel method estimator of the spatial modal regression for functional regressors is proposed. We establish, under some general mixing conditions, the $$L^p$$ L p -consistency and the asymptotic normality of the estimator. The performance of the proposed estimator is illustrated in a real data application. Copyright Springer-Verlag Berlin Heidelberg 2015
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Asymptotic properties of the Kernel Estimate of spatial conditional mode when the regressor is functional
AStA Advances in Statistical Analysis, 2015Co-Authors: S. Dabo-niang, Zoulikha Kaid, Ali LaksaciAbstract:The Kernel method estimator of the spatial modal regression for functional regressors is proposed. We establish, under some general mixing conditions, the $$L^p$$ L p -consistency and the asymptotic normality of the estimator. The performance of the proposed estimator is illustrated in a real data application.
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Nonparametric Quantile Regression Estimation for Functional Dependent Data
Communications in Statistics - Theory and Methods, 2012Co-Authors: S. Dabo-niang, Ali LaksaciAbstract:Let (X i , Y i ) i=1,..., n be a sequence of strongly mixing random variables valued in ℱ × ℝ, where ℱ is a semi-metric space. We consider the problem of estimating the quantile regression function of Y i given X i . The principal aim of the article is to prove the consistency in L p norm of the proposed Kernel Estimate. The usefulness of the estimation is illustrated by a real data application where we are interested in forecasting hourly ozone concentration in the south-east of French.
George G Roussas - One of the best experts on this subject based on the ideXlab platform.
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asymptotic normality of the Kernel Estimate of a probability density function under association
Statistics & Probability Letters, 2000Co-Authors: George G RoussasAbstract:The sole purpose of this paper is to establish asymptotic normality of the usual Kernel Estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. In much of the discussions and derivations, the term association is used to include both positively and negatively associated random variables. The method of proof follows the familiar pattern for dependent situations of using large and small blocks. A result made available in the literature recently is instrumental in the derivations.
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exact rates of almost sure convergence of a recursive Kernel Estimate of a probability densiy function application to regression and hazard rate estimation
Journal of Nonparametric Statistics, 1992Co-Authors: George G RoussasAbstract:Let X1…, X n be a random sample of R d -valued random variables from the probability density function f, and let f n *(x) be a recursive Kernel Estimate of f(x) based on this random sample. Conditions are given under which the exact rates of almost sure convergence of f n *(x) to f(x) are determined. This is done both for d≦1 and also for the special case d = 1. These results are suitably used to establish exact rates for almost sure convergence of a recursive Estimate m n *(x) of the regression function m(x). A further application yields exact rates of almost sure convergence of a recursive Estimate r n (x) of the hazard rate r(x).
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Kernel Estimates under association: strong uniform consistency
Statistics & Probability Letters, 1991Co-Authors: George G RoussasAbstract:Abstract Let X1, X2,… be associated random variables forming a strictly stationary sequence, and let f be the probability density function of X1. For r ⩾ 0 integer, let f(r) be the rth order derivative of f. Under suitable regularity conditions on a Kernel function K, a sequence of bandwidths {hn}, the derivatives f(s), s = 0, 1,…, r, and the covariances Cov(X1, Xi), i ⩾ 2, the usual Kernel Estimate of f(r)(x) is shown to be strongly consistent, uniformly in x. An application is also presented in the estimation of the hazard rate. Finally, certain covergence rates are also discussed.
S. Dabo-niang - One of the best experts on this subject based on the ideXlab platform.
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A new spatial regression estimator in the multivariate context
Comptes rendus de l'Académie des sciences. Série I Mathématique, 2015Co-Authors: S. Dabo-niang, Anne-françoise Yao, Camille TernynckAbstract:In this note, we propose a nonparametric spatial estimator of the regression function View the MathML sourcex→r(x):=E[Yi|Xi=x],x∈Rd, of a stationary (d+1)(d+1)-dimensional spatial process View the MathML source{(Yi,Xi),i∈ZN}, at a point located at some station j. The proposed estimator depends on two Kernels in order to control both the distance between observations and the spatial locations. Almost complete convergence and consistency in LqLq norm (q∈N⁎)(q∈N⁎) of the Kernel Estimate are obtained when the sample considered is an α-mixing sequence.
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Asymptotic properties of the Kernel Estimate of spatial conditional mode when the regressor is functional
AStA Advances in Statistical Analysis, 2015Co-Authors: S. Dabo-niang, Zoulikha Kaid, Ali LaksaciAbstract:The Kernel method estimator of the spatial modal regression for functional regressors is proposed. We establish, under some general mixing conditions, the $$L^p$$ L p -consistency and the asymptotic normality of the estimator. The performance of the proposed estimator is illustrated in a real data application.
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Consistency of a nonparametric conditional mode estimator for random fields
Statistical Methods & Applications, 2014Co-Authors: S. Dabo-niang, S. A. Ould Abdi, A. Ould Abdi, A. DiopAbstract:Given a stationary multidimensional spatial process $$\left\{ Z_{\mathbf{i}}=\left( X_{\mathbf{i}},\ Y_{\mathbf{i}}\right) \in \mathbb R ^d\right. \left. \times \mathbb R ,\mathbf{i}\in \mathbb Z ^{N}\right\} $$ Z i = X i , Y i ∈ R d × R , i ∈ Z N , we investigate a Kernel Estimate of the spatial conditional mode function of the response variable $$Y_{\mathbf{i}}$$ Y i given the explicative variable $$X_{\mathbf{i}}$$ X i . Consistency in $$L^p$$ L p norm and strong convergence of the Kernel Estimate are obtained when the sample considered is a $$\alpha $$ α -mixing sequence. An application to real data is given in order to illustrate the behavior of our methodology.
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Nonparametric Quantile Regression Estimation for Functional Dependent Data
Communications in Statistics - Theory and Methods, 2012Co-Authors: S. Dabo-niang, Ali LaksaciAbstract:Let (X i , Y i ) i=1,..., n be a sequence of strongly mixing random variables valued in ℱ × ℝ, where ℱ is a semi-metric space. We consider the problem of estimating the quantile regression function of Y i given X i . The principal aim of the article is to prove the consistency in L p norm of the proposed Kernel Estimate. The usefulness of the estimation is illustrated by a real data application where we are interested in forecasting hourly ozone concentration in the south-east of French.
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Consistency of a nonparametric conditional quantile estimator for random fields
Mathematical Methods of Statistics, 2010Co-Authors: S. A. Ould Abdi, S. Dabo-niang, A. Diop, A. Ould AbdiAbstract:Given a stationary multidimensional spatial process ( Z _ i = ( X _ i , Y _ i ) ∈ ℝ^ d × ℝ, i ∈ ℤ^ N ), we investigate a Kernel Estimate of the spatial conditional quantile function of the response variable Y _ i given the explicative variable X _ i . Almost complete convergence and consistency in L ^2 r norm ( r ∈ ℕ*) of the Kernel Estimate are obtained when the sample considered is an α -mixing sequence.
Jeffrey L. Solka - One of the best experts on this subject based on the ideXlab platform.
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A qualitative analysis of the resistive grid Kernel estimator
Pattern Recognition Letters, 1994Co-Authors: Wendy L. Poston, George W. Rogers, Carey E. Priebe, Jeffrey L. SolkaAbstract:Abstract The ability to Estimate a probability density function from random data has applications in discriminant analysis and pattern recognition problems. A resistive grid Kernel estimator (RGKE) is described which is suitable for hardware implementation. The one-dimensional linear RGKE is compared to a Kernel Estimate using Gaussian Kernels, and simulations are presented using both continuous and quantized data. The nonlinear form of the RGKE is shown to have desirable properties, such as the ability to detect discontinuities in the density function.
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Resistive Grid Kernel Estimator (RGKE)
1992Co-Authors: Wendy L. Poston, George W. Rogers, Carey E. Priebe, Jeffrey L. SolkaAbstract:Abstract : The ability to Estimate a probability density function from random data has applications in discriminant analysis and pattern recognition problems. A resistive grid Kernel estimator (RGKE) is described that is suitable for hardware implementation. The one-dimensional linear RGKE is compared to a Kernel Estimate using Gaussian Kernels, and simulations are presented using both continuous and quantized data. The nonlinear form of the RGKE is shown to have desirable properties, such as the ability to detect discontinuities in the density function.
Elias Ould Said - One of the best experts on this subject based on the ideXlab platform.
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A note on the conditional density Estimate in single functional index model
Statistics and Probability Letters, 2010Co-Authors: Said Attaoui, Ali Laksaci, Elias Ould SaidAbstract:In this paper, we consider estimation of the conditional density of a scalar response variable given a Hilbertian random variable when the observations are linked with a single-index structure. We establish the pointwise and the uniform almost complete convergence (with the rate) of the Kernel Estimate of this model. As an application, we show how our result can be applied in the prediction problem via the conditional mode Estimate. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is also discussed but not attacked.
