The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
I. Iglewska–nowak - One of the best experts on this subject based on the ideXlab platform.
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A continuous spherical wavelet transform for C(Sn)
Applied and Computational Harmonic Analysis, 2019Co-Authors: I. Iglewska–nowakAbstract:Abstract In the present paper, a wavelet family over the n-dimensional sphere is constructed such that for each scale the wavelet is a polynomial and the inverse wavelet transform of a continuous function converges in the Supremum Norm.
V Subburayan - One of the best experts on this subject based on the ideXlab platform.
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A Robust Computational Method for System of Singularly Perturbed Differential Difference Equations with Discontinuous Convection Coefficients
International Journal of Computational Methods, 2016Co-Authors: V SubburayanAbstract:In this paper, a standard numerical method with piecewise linear interpolation on Shishkin mesh is suggested to solve a weakly coupled system of singularly perturbed boundary value problem for second-order ordinary differential difference equations with discontinuous convection coefficients and source terms. An error estimate is derived by using the Supremum Norm and it is of almost first-order convergence. Numerical results are provided to illustrate the theoretical results.
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a parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient
Arab Journal of Mathematical Sciences, 2016Co-Authors: V SubburayanAbstract:Abstract In this paper a standard numerical method with piecewise linear interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problem for second order ordinary delay differential equations with discontinuous convection coefficient and source term. An error estimate is derived by using the Supremum Norm and it is of almost first order convergence. Numerical results are provided to illustrate the theoretical results.
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Parameter Uniform Numerical Method for Third Order Singularly Perturbed Turning Point Problems Exhibiting Boundary Layers
International Journal of Applied and Computational Mathematics, 2015Co-Authors: N. Geetha, Ayyadurai Tamilselvan, V SubburayanAbstract:In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve singularly perturbed third order differential equations with a turning point exhibiting boundary layers. An error estimate is derived by using Supremum Norm. Numerical results are provided to illustrate the theoretical results.
Borislav R. Draganov - One of the best experts on this subject based on the ideXlab platform.
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Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator
Periodica Mathematica Hungarica, 2020Co-Authors: Borislav R. DraganovAbstract:We establish direct estimates of the rate of weighted simultaneous approximation by the Szász–Mirakjan operator for smooth functions in the Supremum Norm on the non-negative semi-axis. We consider Jacobi-type weights. The estimates are stated in terms of appropriate moduli of smoothness or K -functionals.
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Direct Estimates of the Weighted Simultaneous Approximation by the Baskakov Operator
Results in Mathematics, 2020Co-Authors: Borislav R. DraganovAbstract:We establish direct estimates of the rate of weighted simultaneous approximation by the Baskakov operator for smooth functions in the Supremum Norm on the non-negative semi-axis. We consider Jacobi-type weights. The estimates are stated in terms of appropriate moduli of smoothness or K-functionals.
William Weimin Yoo - One of the best experts on this subject based on the ideXlab platform.
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adaptive Supremum Norm posterior contraction wavelet spike and slab and anisotropic besov spaces
arXiv: Statistics Theory, 2017Co-Authors: William Weimin Yoo, V. Rivoirard, J. RousseauAbstract:Supremum Norm loss is intuitively more meaningful to quantify function estimation error in statistics. In the context of multivariate nonparametric regression with unknown error, we propose a Bayesian procedure based on spike-and-slab prior and wavelet projections to estimate the regression function and all its mixed partial derivatives. We show that their posterior distributions contract to the truth optimally and adaptively under Supremum-Norm loss. The master theorem through tests with exponential errors used in Bayesian nonparametrics was not adequate to deal with this problem, and we developed a new idea such that posterior under the regression model is systematically reduced to a posterior arising from some quasi-white noise model, where the latter model greatly simplifies our rate calculations. Hence, this paper takes the first step in showing explicitly how one can translate results from white noise to regression model in a Bayesian setting.
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Adaptive Supremum Norm Posterior Contraction : Spike-and-Slab Priors and Anisotropic Besov Spaces
arXiv: Statistics Theory, 2017Co-Authors: William Weimin Yoo, J. Rousseau, V. RivoirardAbstract:Supremum Norm loss is intuitively more meaningful to quantify estimation error in statistics. In the context of multivariate nonparametric regression with unknown error, we propose a Bayesian procedure based on spike-and-slab prior and wavelet projections to estimate the regression function f and its derivatives. We show that their posteriors contract to the truth optimally and adaptively under Supremum Norm loss. We discovered that there is a lower limit in the range of smoothness that we can adapt to and this limit grows with dimension of the function's domain. The master theorem through exponential error test used in Bayesian nonparametrics was not adequate to deal with this problem, and we developed a new idea by bounding posterior under the regression model with a posterior arising from some quasi-white noise model, where the latter model greatly simplifies our calculations.
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Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression
The Annals of Statistics, 2016Co-Authors: William Weimin Yoo, Subhashis GhosalAbstract:In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of tensor product of B-splines with Normal basis coefficients as a prior for f, and the error variance is either estimated using the empirical Bayes approach or is endowed with a suitable prior in a hierarchical Bayes approach. We establish pointwise, L2 and Supremum Norm posterior contraction rates for f and its mixed partial derivatives, and show that they coincide with the minimax rates. Our results cover even the anisotropic situation, where the true regression function may have different smoothness in different directions. Using the convergence bounds, we show that pointwise, L2 and Supremum Norm credible sets for f and its mixed partial derivatives have guaranteed frequentist coverage with optimal size. New results on tensor products of B-splines are also obtained in the course.
Subhashis Ghosal - One of the best experts on this subject based on the ideXlab platform.
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Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression
The Annals of Statistics, 2016Co-Authors: William Weimin Yoo, Subhashis GhosalAbstract:In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of tensor product of B-splines with Normal basis coefficients as a prior for f, and the error variance is either estimated using the empirical Bayes approach or is endowed with a suitable prior in a hierarchical Bayes approach. We establish pointwise, L2 and Supremum Norm posterior contraction rates for f and its mixed partial derivatives, and show that they coincide with the minimax rates. Our results cover even the anisotropic situation, where the true regression function may have different smoothness in different directions. Using the convergence bounds, we show that pointwise, L2 and Supremum Norm credible sets for f and its mixed partial derivatives have guaranteed frequentist coverage with optimal size. New results on tensor products of B-splines are also obtained in the course.