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Maxisets for density estimation on R
 Math. Methods of Statist., n
, 2006
"... The problem of density estimation on R is considered. Adopting the maxiset point of view, we focus on performance of adaptive procedures. Any rule which consists in neglecting the wavelet empirical coefficients smaller than a sequence of thresholds vn will be called an elitist rule. We prove that fo ..."
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Cited by 9 (3 self)
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The problem of density estimation on R is considered. Adopting the maxiset point of view, we focus on performance of adaptive procedures. Any rule which consists in neglecting the wavelet empirical coefficients smaller than a sequence of thresholds vn will be called an elitist rule. We prove
MAXISETS FOR MODEL SELECTION
"... We address the statistical issue of determining the maximal spaces (maxisets) where model selection procedures attain a given rate of convergence. By considering first general dictionaries, then orthonormal bases, we characterize these maxisets in terms of approximation spaces. These results are i ..."
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Cited by 1 (0 self)
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We address the statistical issue of determining the maximal spaces (maxisets) where model selection procedures attain a given rate of convergence. By considering first general dictionaries, then orthonormal bases, we characterize these maxisets in terms of approximation spaces. These results
Maxiset in supnorm for kernel estimators
, 2008
"... In the Gaussian white noise model, we study the estimation of an unknown multidimensional function f in the uniform norm by using kernel methods. The performances of procedures are measured by using the maxiset point of view: we determine the set of functions which are well estimated (at a prescrib ..."
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Cited by 3 (2 self)
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In the Gaussian white noise model, we study the estimation of an unknown multidimensional function f in the uniform norm by using kernel methods. The performances of procedures are measured by using the maxiset point of view: we determine the set of functions which are well estimated (at a
Bayesian modelization of sparse sequences and maxisets for bayes rules
, 2003
"... In this paper, our aim is to estimate sparse sequences in the framework of the heteroscedastic white noise model. To model sparsity, we consider a Bayesian model composed of a mixture of a heavytailed density and a point mass at zero. To evaluate the performance of the Bayes rules (the median or th ..."
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Cited by 7 (5 self)
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or the mean of the posterior distribution), we exploit an alternative to the minimax setting developed in particular by Kerkyacharian and Picard: we determine the maxisets for each of these estimators. Using this approach, we compare the performance of Bayesian procedures with thresholding ones. Furthermore
Large variance Gaussian priors in Bayesian nonparametric estimation: a maxiset approach
 Mathematical Methods of Statistics
, 2006
"... In this paper we compare wavelet Bayesian rules taking into account the sparsity of the signal with priors which are combinations of a Dirac mass with a standard distribution properly normalized. To perform these comparisons, we take the maxiset point of view: i. e. we consider the set of functions ..."
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Cited by 4 (3 self)
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In this paper we compare wavelet Bayesian rules taking into account the sparsity of the signal with priors which are combinations of a Dirac mass with a standard distribution properly normalized. To perform these comparisons, we take the maxiset point of view: i. e. we consider the set of functions
Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach
 APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
, 2013
"... ..."
Maxibay_rev.pdf" Large variance Gaussian priors in Bayesian nonparametric estimation: a maxiset approach ∗
, 2005
"... In this paper we compare wavelet Bayesian rules taking into account the sparsity of the signal with priors which are combinations of a Dirac mass with a standard distribution properly normalized. To perform these comparisons, we take the maxiset point of view: i. e. we consider the set of functions ..."
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In this paper we compare wavelet Bayesian rules taking into account the sparsity of the signal with priors which are combinations of a Dirac mass with a standard distribution properly normalized. To perform these comparisons, we take the maxiset point of view: i. e. we consider the set of functions
Adaptive estimation on anisotropic Hölder spaces Part II. Partially adaptive case
, 2006
"... In this paper, we consider a particular case of adaptation. Let us recall that, in the first paper “Fully case”, a large collecton of anisotropic Hölder spaces is fixed and the goal is to construct an adaptive estimator with respect to the absolutely unknown smoothness parameter. Here the problem is ..."
Prépublication n o 822
, 2003
"... The problem of density estimation on R is concerned. Adopting the maxiset point of view, the aim of this paper is threefold. Firstly, we prove that the maxiset of any elitist rule is contained in the intersection of a Besov space and a weak Besov space. Secondly, we provide an adaptive procedure for ..."
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The problem of density estimation on R is concerned. Adopting the maxiset point of view, the aim of this paper is threefold. Firstly, we prove that the maxiset of any elitist rule is contained in the intersection of a Besov space and a weak Besov space. Secondly, we provide an adaptive procedure
on Full Lebesgue Measure Sets ∗
, 2004
"... We consider the nonparametric estimation of a function that is observed in white noise after convolution with a boxcar, the indicator of an interval (−a, a). In a recent paper Johnstone et al. (2004) have developped a wavelet deconvolution algorithm (called WaveD) that can be used for “certain ” box ..."
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of WaveD that are valid for “almost all ” boxcar convolution (i.e. when a ∈ A where A is a full Lebesgue measure set). We propose (i) a tuning inspired from Minimax theory over Besov spaces; (ii) a tuning inspired from Maxiset theory providing similar rates as for BA numbers. Asymptotic theory informs
Results 1  10
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71