Propagation-Separation Approach for Local Likelihood Estimation

By Jörg Polzehl, Vladimir Spokoiny. 2006

221 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Statistics and Probability

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Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, methodology): “ 2p ne zn 1=2. Then it holds IP eu2 0( p z n) 1 4p ne zn: (5.12) In particular, the choice z n= x n+ log(p n) with x n= Clogn provides IP eu2 0( p z n) 1 4e xn: (5.13) Proof. We use the bound from Polzehl and Spokoiny (2006) IP M nK(ue j;uj) >z n 2e zn: This yields IP ue2 0( p z n) 1 2e zn p n: ”
Critical dimension in the semiparametric Bernstein—von Mises theorem (2014, unknown): “We use the following bound from [23]:”
Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights (2009, methodology): “Polzehl and Spokoiny used the Kullback-Leibler divergence between the estimates4 as a test statistic of hypotheses [30].”
Localizing Temperature Risk (2016, unknown): “(9) To guarantee the feasibility of the tests, we need moment bounds and con dence sets for the LR that will guarantee that the MLE is concentrated in the level set of the likelihood ratio process (indexed by the number of observations) around the true parameter, see Polzehl and Spokoiny (2006) and ”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, methodology): “4.1): neighborhood filter (Buades et al. 2005), NL-means algorithm (Buades et al. 2005), Adaptive Weights Smoothing (AWS) (Polzehl and Spokoiny 2000, 2005), Exemplar-based (Kervrann and Boulanger 2005, 2006, 2008), scale and rotation invariant (Lou et al. 2008a; Zimmer et al. 2008) Higher-order…”
Oriented Object Proposals (2015, background): “(1) can be achieved by maximizing the likelihood of a set of neighbor pixels [13, 23]:”
Local quantile regression (2010, methodology): “nt ingredient of the method is the consistency check. The Lepski method suggests to use the dierence e k(x) e ‘(x) as a test statistic; see e.g. Lepski et al. (1997). We follow the suggestion from Polzehl and Spokoiny (2006) and apply a localized likelihood ratio type test. More precisely, the local”
Inhomogeneous Dependence Modeling with Time-Varying Copulae (2009, unknown): “introduced by Polzehl and Spokoiny (2006) , Belomestny and Spokoiny (2007) and Spokoiny (2007).”
NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising (2015, background): “and [53] by introducing a weighted maximum likelihood”