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1,484
On spatial adaptive estimation of nonparametric regression
- Math. Meth. Statistics
, 1997
"... The paper is devoted to developing spatial adaptive estimates for restoring functions from noisy observations. We show that the traditional least square (piecewise polynomial) estimate equipped with adaptively adjusted window possesses simultaneously many attractive adaptive properties, namely, 1) i ..."
Abstract
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Cited by 76 (6 self)
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The paper is devoted to developing spatial adaptive estimates for restoring functions from noisy observations. We show that the traditional least square (piecewise polynomial) estimate equipped with adaptively adjusted window possesses simultaneously many attractive adaptive properties, namely, 1
Sensitivity Analysis of a Spatially-Adaptive Estimator for Data Fusion
, 2002
"... We analyze the parametric sensitivity of a spatially-adaptive multiscale data fusion method. The fusion problem is formulated as a recursive estimation problem in scale and space using a set of 1-D Kalman filters. The overall filter accommodates data acquired at different resolutions and missing dat ..."
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We analyze the parametric sensitivity of a spatially-adaptive multiscale data fusion method. The fusion problem is formulated as a recursive estimation problem in scale and space using a set of 1-D Kalman filters. The overall filter accommodates data acquired at different resolutions and missing
Ideal spatial adaptation by wavelet shrinkage
- Biometrika
, 1994
"... With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic ad ..."
Abstract
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Cited by 1269 (5 self)
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advantages over traditional linear estimation by nonadaptive kernels � however, it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone. We describe a new principle for spatially-adaptive estimation: selective wavelet reconstruction. Weshowthatvariableknot
Spatially-adaptive penalties for spline fitting
- Australian and New Zealand Journal of Statistics
, 2000
"... We study spline fitting with a roughness penalty that adapts to spatial heterogene-ity in the regression function. Our estimates are pth degree piecewise polynomials with p − 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty ..."
Abstract
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Cited by 55 (7 self)
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We study spline fitting with a roughness penalty that adapts to spatial heterogene-ity in the regression function. Our estimates are pth degree piecewise polynomials with p − 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty
SPATIALLY ADAPTIVE SUPPORT AS A LEADING MODEL-SELECTION TOOL FOR IMAGE FILTERING
, 2008
"... One of the promising recent directions in nonparametric regression concerns the spatially adaptive estimation, which can be treated as an extended model selection problem where the basis as well as the basis supports are selected simultaneously. Our research ..."
Abstract
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Cited by 1 (1 self)
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One of the promising recent directions in nonparametric regression concerns the spatially adaptive estimation, which can be treated as an extended model selection problem where the basis as well as the basis supports are selected simultaneously. Our research
On Spatial Adaptive Nonparametric Estimation of Functions Satisfying Differential Inequalities
, 1996
"... The paper is devoted to developing spatial adaptive estimates of the signals satisfying linear differential inequalities with unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes usual in the nonparametric regression problem; more ..."
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The paper is devoted to developing spatial adaptive estimates of the signals satisfying linear differential inequalities with unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes usual in the nonparametric regression problem
Computational Models of Sensorimotor Integration
- SCIENCE
, 1997
"... The sensorimotor integration system can be viewed as an observer attempting to estimate its own state and the state of the environment by integrating multiple sources of information. We describe a computational framework capturing this notion, and some specific models of integration and adaptati ..."
Abstract
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Cited by 424 (12 self)
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and adaptation that result from it. Psychophysical results from two sensorimotor systems, subserving the integration and adaptation of visuo-auditory maps, and estimation of the state of the hand during arm movements, are presented and analyzed within this framework. These results suggest that: (1) Spatial
Minimax Estimation via Wavelet Shrinkage
, 1992
"... We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly minim ..."
Abstract
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Cited by 321 (29 self)
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method (kernel, smoothing spline, sieve,:::) in a minimax sense. Variants of our method based on simple threshold nonlinearities are nearly minimax. Our method possesses the interpretation of spatial adaptivity: it reconstructs using a kernel which mayvary in shape and bandwidth from point to point
Spatially Adaptive Splines for Statistical Linear Inverse Problems
, 2002
"... This paper introduces a new nonparametric estimator based on penalized regression splines for linear operator equations when the data are noisy. A local roughness penalty that relies on local support properties of B-splines is introduced in order to deal with spatial heterogeneity of the function to ..."
Abstract
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Cited by 4 (2 self)
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simulation study. Key Words: linear inverse problems, integral equations, deconvolution, regularization, local roughness penalties, spatially adaptive estimators, regression splines, convergence. 1 2 CARDOT 1. INTRODUCTION
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