The Experts below are selected from a list of 1479 Experts worldwide ranked by ideXlab platform
Dragi Anevski - One of the best experts on this subject based on the ideXlab platform.
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Limit properties of the monotone rearrangement for density and regression function estimation
Bernoulli, 2019Co-Authors: Dragi Anevski, Anne-laure FougèresAbstract:The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Pólya as a sorting device for functions. Assuming that x is a monotone function and that an estimate x n of x is given, consider the monotone rearrangementˆxrearrangementˆ rearrangementˆx n of x n. This new estimator is shown to be uniformly consistent as soon as x n is. Under suitable assumptions, Pointwise Limit distribution results forˆxforˆ forˆx n are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed. Asymptotics for rearrangement estimators with vanishing derivatives are also obtained in these two contexts.
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Monotone spectral density estimation
Annals of Statistics, 2011Co-Authors: Dragi Anevski, Philippe SoulierAbstract:We propose two estimators of a unimodal or monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive Pointwise Limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.
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Limit properties of the monotone rearrangement for density and regression function estimation
2008Co-Authors: Dragi Anevski, Anne-laure FougèresAbstract:The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Po lya as a sorting device for functions. As- suming that x is a monotone function and that an estimate xn of x is given, consider the monotone rearrangement xˆn of xn. This new estimator is shown to be uniformly consistent. Under suitable as- sumptions, Pointwise Limit distribution results for xˆn are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed.
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A general asymptotic scheme for inference under order restrictions
The Annals of Statistics, 2006Co-Authors: Dragi Anevski, Ola HossjerAbstract:Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various Pointwise Limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.
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monotone regression and density function estimation at a point of discontinuity
Journal of Nonparametric Statistics, 2002Co-Authors: Dragi Anevski, Ola HossjerAbstract:Pointwise Limit distribution results are given for the isotonic regression estimator at a point of discontinuity. The cases treated are independent data, - and f -mixing data and subordinated Gaussian long range dependent data. Pointwise Limit results for the nonparametric maximum likelihood estimator of a monotone density are given at a point of discontinuity, for independent data. The Limit distributions are non-standard and differ from the ones obtained for differentiable regression and density functions.
Sandro Levi - One of the best experts on this subject based on the ideXlab platform.
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strong uniform continuity
Journal of Mathematical Analysis and Applications, 2009Co-Authors: Gerald Beer, Sandro LeviAbstract:Abstract Let B be an ideal of subsets of a metric space 〈 X , d 〉 . This paper considers a strengthening of the notion of uniform continuity of a function restricted to members of B which reduces to ordinary continuity when B consists of the finite subsets of X and agrees with uniform continuity on members of B when B is either the power set of X or the family of compact subsets of X. The paper also presents new function space topologies that are well suited to this strengthening. As a consequence of the general theory, we display necessary and sufficient conditions for continuity of the Pointwise Limit of a net of continuous functions.
Hikmet Koyunbakan - One of the best experts on this subject based on the ideXlab platform.
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reconstruction formula for the potential function of sturm liouville problem with eigenparameter boundary condition
Inverse Problems in Science and Engineering, 2010Co-Authors: Etibar S Panakhov, Hikmet KoyunbakanAbstract:It is known that the uniqueness of potential function of the Sturm–Liouville problem can be shown from the nodal points. In this article, we solve the inverse nodal problem of the reconstruction of the potential function q from the nodal data by a Pointwise Limit. We show that this convergence is in the L1. It is mentioned that this method is based on the works of Law and Yang, but we have applied the method for the Sturm–Liouville problem depending on eigenparameter boundary conditions.
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Reconstruction of potential function and its derivatives for Sturm–Liouville problem with eigenvalues in boundary condition
Inverse Problems in Science and Engineering, 2010Co-Authors: Emrah Yilmaz, Hikmet KoyunbakanAbstract:The purpose of this article is solving inverse nodal problem for Sturm–Liouville equation with a boundary condition depending on spectral parameter. Taking into account Law and Chen's method, we construct the potential function q and its derivatives by using nodal data. We give several lemmas in order to complete proof of the main theorem. Especially, we obtain an explicit formula for potential function and its derivatives from the nodal data by a Pointwise Limit.
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Reconstruction formula for the potential function of Sturm–Liouville problem with eigenparameter boundary condition
Inverse Problems in Science and Engineering, 2010Co-Authors: Etibar S Panakhov, Hikmet KoyunbakanAbstract:It is known that the uniqueness of potential function of the Sturm–Liouville problem can be shown from the nodal points. In this article, we solve the inverse nodal problem of the reconstruction of the potential function q from the nodal data by a Pointwise Limit. We show that this convergence is in the L1. It is mentioned that this method is based on the works of Law and Yang, but we have applied the method for the Sturm–Liouville problem depending on eigenparameter boundary conditions.
Irene M. Gamba - One of the best experts on this subject based on the ideXlab platform.
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Viscosity Approximating Solutions to ODE Systems That Admit Shocks, and Their Limits
Advances in Applied Mathematics, 1994Co-Authors: Irene M. GambaAbstract:We study nonlinear systems of ordinary differential equations that arise when considering stationary one-dimensional systems of conservation laws with forcing terms defined in a bounded interval. We construct weak entropy solutions of bounded variation which are Pointwise and L^1 Limits of solutions of regularized, i.e., viscous, systems, where the Limit is taken in the viscosity parameter. In particular, no oscillations occur either for the viscous solutions or for the inviscid one. We also discuss the possible formation of boundary layers when boundary values are prescribed for the viscous regularized equations. As applications, first we show the existence of transonic solutions of bounded variation with strong shocks for the equation of stationary gas flow in a duct of variable area as a Pointwise Limit of artificial viscosity solutions. We analyze their properties depending on the kind of duct as well as on the boundary data of the regularized problem. Second we show that the model applies to the hydrodynamic modeling for semiconductor devices for some particular heat conduction terms and added diffusion to the energy equation. In particular, we show that under the assumption of bounds for the state variables, there exists a regular solution for that particular viscous heat conducting model. Also, if the bounds for the state variables are uniform in the vanishing parameters, we obtain the existence of an inviscid weak entropy solution of bounded variation as a Pointwise Limit of the regular ones.
Ola Hossjer - One of the best experts on this subject based on the ideXlab platform.
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A general asymptotic scheme for inference under order restrictions
The Annals of Statistics, 2006Co-Authors: Dragi Anevski, Ola HossjerAbstract:Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various Pointwise Limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.
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monotone regression and density function estimation at a point of discontinuity
Journal of Nonparametric Statistics, 2002Co-Authors: Dragi Anevski, Ola HossjerAbstract:Pointwise Limit distribution results are given for the isotonic regression estimator at a point of discontinuity. The cases treated are independent data, - and f -mixing data and subordinated Gaussian long range dependent data. Pointwise Limit results for the nonparametric maximum likelihood estimator of a monotone density are given at a point of discontinuity, for independent data. The Limit distributions are non-standard and differ from the ones obtained for differentiable regression and density functions.