Gerard Kerkyacharian - Academia.edu (original) (raw)

Gerard Kerkyacharian

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Papers by Gerard Kerkyacharian

Research paper thumbnail of Dicussion on the Meeting on ‘Statistical Approaches to Inverse Problems’

Journal of the Royal Statistical Society Series B: Statistical Methodology, 2004

Research paper thumbnail of Capturing Ridge Functions in High Dimension from Point Queries

Research paper thumbnail of Minimax or Maxisets?

Research paper thumbnail of Limit of the quadratic risk in density estimation using linear methods

Statistics & Probability Letters, 1997

Research paper thumbnail of On the minimax optimality of block thresholded wavelet estimators with long memory data

Journal of Statistical Planning and Inference, 2007

Research paper thumbnail of Universal Near Minimaxity of

We discuss a method for curve estimation based on n noisy data; one translates the empirical wave... more We discuss a method for curve estimation based on n noisy data; one translates the empirical wavelet coefficients towards the origin by an amount v210g(n) . aj.,fii. The method is nearly minimax for a wide variety of loss functions----e.g. pointwise error, global error measured in LP norms, pointwise and global error in estimation of derivatives-and for a wide range of smoothness classes, including standard HOlder classes, Sobolev classes, and Bounded Variation. This is a broader near-optimality than anything previously proposed in the minimax literature. The theory underlying the method exploits a correspondence between statistical ques­ tions and questions of optimal recovery and information-based complexity. This paper contains a detailed proof of the result announced in Donoho, Johnstone, Kerkyacharian & Picard (1995).

Research paper thumbnail of Kernel and wavelet density estimators on manifolds and more general metric spaces

Research paper thumbnail of Gaussian Bounds for the Heat Kernel Associated to Prolate Spheroidal Wave Functions with Applications

Constructive Approximation

Research paper thumbnail of 1 Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds

Research paper thumbnail of Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex

Constructive Approximation, 2019

Research paper thumbnail of Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators

Journal of Fourier Analysis and Applications, 2019

Research paper thumbnail of Gaussian bounds for the heat kernels on the ball and the simplex: classical approach

Research paper thumbnail of Regularity of Gaussian Processes on Dirichlet Spaces

Constructive Approximation, 2018

Research paper thumbnail of Wavelet Shrinkage: Asymptopia?

Journal of the Royal Statistical Society: Series B (Methodological), 1995

Research paper thumbnail of Hardy spaces associated with non-negative self-adjoint operators

Research paper thumbnail of Large deviations and the Strassen theorem in H�lder norm

Research paper thumbnail of Lecture Notes in Statistics Vol 129

Research paper thumbnail of Needvd: second generation wavelets for estimation in inverse problems

Research paper thumbnail of Universal Near Minimaxity of Wavelet Shrinkage

Festschrift for Lucien Le Cam, 1997

Research paper thumbnail of Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces

Transactions of the American Mathematical Society, 2014

Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of indices are d... more Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincaré inequality. This leads to a heat kernel with small time Gaussian bounds and Hölder continuity, which play a central role in this article. Frames with band limited elements of sub-exponential space localization are developed, and frame and heat kernel characterizations of Besov and Triebel-Lizorkin spaces are established. This theory, in particular, allows the development of Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifolds, and other settings.

Research paper thumbnail of Dicussion on the Meeting on ‘Statistical Approaches to Inverse Problems’

Journal of the Royal Statistical Society Series B: Statistical Methodology, 2004

Research paper thumbnail of Capturing Ridge Functions in High Dimension from Point Queries

Research paper thumbnail of Minimax or Maxisets?

Research paper thumbnail of Limit of the quadratic risk in density estimation using linear methods

Statistics & Probability Letters, 1997

Research paper thumbnail of On the minimax optimality of block thresholded wavelet estimators with long memory data

Journal of Statistical Planning and Inference, 2007

Research paper thumbnail of Universal Near Minimaxity of

We discuss a method for curve estimation based on n noisy data; one translates the empirical wave... more We discuss a method for curve estimation based on n noisy data; one translates the empirical wavelet coefficients towards the origin by an amount v210g(n) . aj.,fii. The method is nearly minimax for a wide variety of loss functions----e.g. pointwise error, global error measured in LP norms, pointwise and global error in estimation of derivatives-and for a wide range of smoothness classes, including standard HOlder classes, Sobolev classes, and Bounded Variation. This is a broader near-optimality than anything previously proposed in the minimax literature. The theory underlying the method exploits a correspondence between statistical ques­ tions and questions of optimal recovery and information-based complexity. This paper contains a detailed proof of the result announced in Donoho, Johnstone, Kerkyacharian & Picard (1995).

Research paper thumbnail of Kernel and wavelet density estimators on manifolds and more general metric spaces

Research paper thumbnail of Gaussian Bounds for the Heat Kernel Associated to Prolate Spheroidal Wave Functions with Applications

Constructive Approximation

Research paper thumbnail of 1 Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds

Research paper thumbnail of Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex

Constructive Approximation, 2019

Research paper thumbnail of Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators

Journal of Fourier Analysis and Applications, 2019

Research paper thumbnail of Gaussian bounds for the heat kernels on the ball and the simplex: classical approach

Research paper thumbnail of Regularity of Gaussian Processes on Dirichlet Spaces

Constructive Approximation, 2018

Research paper thumbnail of Wavelet Shrinkage: Asymptopia?

Journal of the Royal Statistical Society: Series B (Methodological), 1995

Research paper thumbnail of Hardy spaces associated with non-negative self-adjoint operators

Research paper thumbnail of Large deviations and the Strassen theorem in H�lder norm

Research paper thumbnail of Lecture Notes in Statistics Vol 129

Research paper thumbnail of Needvd: second generation wavelets for estimation in inverse problems

Research paper thumbnail of Universal Near Minimaxity of Wavelet Shrinkage

Festschrift for Lucien Le Cam, 1997

Research paper thumbnail of Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces

Transactions of the American Mathematical Society, 2014

Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of indices are d... more Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincaré inequality. This leads to a heat kernel with small time Gaussian bounds and Hölder continuity, which play a central role in this article. Frames with band limited elements of sub-exponential space localization are developed, and frame and heat kernel characterizations of Besov and Triebel-Lizorkin spaces are established. This theory, in particular, allows the development of Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifolds, and other settings.

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