Deconvolution in white noise with a random blurring function

We consider the problem of denoising a function observed after a convolution with a random filter independent of the noise and satisfying some mean smoothness condition depending on an ill posedness coefficient. We establish the minimax rates for the Lp risk over balls of periodic Besov spaces with respect to the level of noise, and we provide an adaptive estimator achieving these rates up to log factors. Simulations were performed to highlight the effects of the ill posedness and of the distribution of the filter on the efficiency of the estimator

Estimation in the convolution structure density model. Part I: oracle inequalities

We study the problem of nonparametric estimation under \bL_p-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on \bR^d. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. In Part I the original pointwise selection rule from a family of "kernel-type" estimators is proposed. For the selected estimator, we prove an \bL_p-norm oracle inequality and several of its consequences. In Part II the problem of adaptive minimax estimation under \bL_p--loss over the scale of anisotropic Nikol'skii classes is addressed. We fully characterize the behavior of the minimax risk for different relationships between regularity parameters and norm indexes in the definitions of the functional class and of the risk. We prove that the selection rule proposed in Part I leads to the construction of an optimally or nearly optimally (up to logarithmic factor) adaptive estimator

Estimation in the convolution structure density model. Part II: adaptation over the scale of anisotropic classes

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on \bR^d, we address the problem of adaptive minimax estimation with \bL_p--loss over the scale of anisotropic Nikol'skii classes. We fully characterize the behavior of the minimax risk for different relationships between regularity parameters and norm indexes in the definitions of the functional class and of the risk. In particular, we show that the boundedness of the function to be estimated leads to an essential improvement of the asymptotic of the minimax risk. We prove that the selection rule proposed in Part I leads to the construction of an optimally or nearly optimally (up to logarithmic factor) adaptive estimator

Market strategies in different stages - How to stimulate organic market development

Organic agriculture generates tangible benefits for both producers and consumers. But it also produces wider public benefits, and it should therefore be a common concern to help the organic sector develop better and faster, rather than just leaving it to market forces

Needlet algorithms for estimation in inverse problems

We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the advantages of localization and multiscale analysis of wavelet representations without losing the stability and computability of the SVD decompositions. To this end we utilize the construction of localized frames (termed "needlets") built upon the SVD bases. We consider two different situations: the "wavelet" scenario, where the needlets are assumed to behave similarly to true wavelets, and the "Jacobi-type" scenario, where we assume that the properties of the frame truly depend on the SVD basis at hand (hence on the operator). To illustrate each situation, we apply the estimation algorithm respectively to the deconvolution problem and to the Wicksell problem. In the latter case, where the SVD basis is a Jacobi polynomial basis, we show that our scheme is capable of achieving rates of convergence which are optimal in the $L_2$ case, we obtain interesting rates of convergence for other $L_p$ norms which are new (to the best of our knowledge) in the literature, and we also give a simulation study showing that the NEED-D estimator outperforms other standard algorithms in almost all situations.Comment: Published at http://dx.doi.org/10.1214/07-EJS014 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lower bounds in the convolution structure density model

International audienceThe aim of the paper is to establish asymptotic lower bounds for the minimax risk in two generalized forms of the density deconvolution problem. The observation consists of an independent and identically distributed (i.i.d.) sample of n random vectors in R d. Their common probability distribution function p can be written as p = (1 − α)f + α[f ⋆ g], where f is the unknown function to be estimated, g is a known function, α is a known proportion, and ⋆ denotes the convolution product. The bounds on the risk are established in a very general minimax setting and for moderately ill posed convolutions. Our results show notably that neither the ill-posedness nor the proportion α play any role in the bounds whenever α ∈ [0, 1), and that a particular inconsistency zone appears for some values of the parameters. Moreover, we introduce an additional boundedness condition on f and we show that the inconsistency zone then disappears

Numerical performances of a warped wavelet estimation procedure for regression in random design

The purpose of this paper is to investigate the numerical performances of the hard thresholding procedure introduced by Kerkyacharian and Picard (2004) for the non-parametric regression model with random design. That construction adopts a new approach by using a wavelet basis warped with a function depending on the design, which enables to estimate regression functions under mild assumptions on the design. We compare our numerical properties to those obtained for other constructions based on hard wavelet thresholding. The performances are evaluated on numerous simulated data sets covering a broad variety of settings including known and unknown design density models, and also on real data sets

The Internet Activities of FiBL

The poster presents the main internet sites maintained by FIBL in 2002: www.fibl.org www.oekolandbau.de http://www.organicxseeds.com

Added value from working together

During the meeting the eight new transnational research projects were presented and potential benefits and constraints of transnational research cooperations in organic food and farming through an ERANET were discussed. Furthermore, the outputs, findings and the "lessons learned" during the 3-year period of the ERA-NET project CORE Organic were presented and discussed

A family of functions with two different spectra of singularities

International audienceOur goal is to study the multifractal properties of functions of a given family which have few non vanishing wavelet coefficients. We compute at each point the pointwise Holder exponent of these functions and also their local Lp regularity, computing the so-called p-exponent. We prove that in the general case the Holder and p exponent are different at each point. We also compute the dimension of the sets where the functions have a given pointwise regularity and prove that these functions are multifractal both from the point of view of Holder and Lp local regularity with different spectra of singularities. Furthermore, we check that multifractal formalism type formulas hold for functions in that family