On Spatial Adaptive Estimation of Nonparametric Regression

By Alexander Goldenshluger. 2004

191 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

A Retrieve-and-Edit Framework for Predicting Structured Outputs (2018, background): “Adaptive kernels for nonparametric regression are well-studied [11] but have mainly focused on learning local smoothness parameters rather than the functional form of the kernel.”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, methodology): “2.1–2.4): Nadaraya-Watson (Cleveland and Devlin 1988; Brown 1963; Savitzky and Golay 1964; Nadaraya 1964; Watson 1964), LPA (Fan and Gijbels 1996; Katkovnik 1976; Loader 1999), Lepski’s approach (Lepski et al. 1997; Spokoiny 1998; Polzehl and Spokoiny 2003), LPA-ICI (Goldenshluger and Nemirovski 199”
Robust multivariate mean estimation: The optimality of trimmed mean (2019, methodology): “Note that the last step of selecting the value of Q is reminiscent of Lepski’s method [19] or the related method “intersection of confidence intervals” by Goldenshluger and Nemirovski [12].”
Optimal Spatial Adaptation for Patch-Based Image Denoising (2006, background): “Following the above discussion, a window selector will be then based on the following pointwise rule [26], [28], [34], [35]”
Local adaptivity to variable smoothness for exemplar-based image denoising and representation (2005, unknown): “Following the above discussion, a window selector is then based on the following pointwise rule [49, 52, 42, 50, 36]: b (xi) = arg max i;n2N fj i;nj : jb ui;n b ui;n0 j % b i;n0 for all 1 n0 < ng : (21)”
Structural adaptation via Lp-norm oracle inequalities (2007, methodology): “, [2,8,24] for the univariate case, and [21,22] for the multivariate case.”
Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images (2007, methodology): “In our approach, we use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation (LPA) Intersection of ConÞdence Intervals (ICI) [26], [24], [21], [18], a technique purposely designed to work accurately with noisy data.”