Conditional Density Estimation by Penalized Likelihood Model Selection and Applications

In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a best model within a collection. We give a general condition on penalty choice that leads to oracle type inequality for the resulting estimate. This construction is applied to two examples of partition-based conditional density models, models in which the conditional density depends only in a piecewise manner from the covariate. The first example relies on classical piecewise polynomial densities while the second uses Gaussian mixtures with varying mixing proportion but same mixture components. We show how this last case is related to an unsupervised segmentation application that has been the source of our motivation to this study.Comment: No. RR-7596 (2011

Thresholding methods to estimate the copula density

This paper deals with the problem of the multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which the knowledge of the regularity of the copula density to be estimated is not necessary. These methods, said to be adaptive, are proved to perform very well when adopting the minimax and the maxiset approaches. Moreover we show that these procedures can be discriminated in the maxiset sense. We produce an estimation algorithm whose qualities are evaluated thanks some simulation. Last, we propose a real life application for financial data

Thresholding methods to estimate the copula density

This paper deals with the problem of the multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which the knowledge of the regularity of the copula density to be estimated is not necessary. These methods, said to be adaptive, are proved to perform very well when adopting the minimax and the maxiset approaches. Moreover we show that these procedures can be discriminated in the maxiset sense. We produce an estimation algorithm whose qualities are evaluated thanks some simulation. Last, we propose a real life application for financial data

Gaussian Mixture Regression model with logistic weights, a penalized maximum likelihood approach

We wish to estimate conditional density using Gaussian Mixture Regression model with logistic weights and means depending on the covariate. We aim at selecting the number of components of this model as well as the other parameters by a penalized maximum likelihood approach. We provide a lower bound on penalty, proportional up to a logarithmic term to the dimension of each model, that ensures an oracle inequality for our estimator. Our theoretical analysis is supported by some numerical experiments

Radon needlet thresholding

We provide a new algorithm for the treatment of the noisy inversion of the Radon transform using an appropriate thresholding technique adapted to a well-chosen new localized basis. We establish minimax results and prove their optimality. In particular, we prove that the procedures provided here are able to attain minimax bounds for any $\mathbb {L}_p$ loss. It s important to notice that most of the minimax bounds obtained here are new to our knowledge. It is also important to emphasize the adaptation properties of our procedures with respect to the regularity (sparsity) of the object to recover and to inhomogeneous smoothness. We perform a numerical study that is of importance since we especially have to discuss the cubature problems and propose an averaging procedure that is mostly in the spirit of the cycle spinning performed for periodic signals

Infestation of the clam Venus verrucosa by Sipunculoidea and the lithophagus bivalve, Gastrochaena dubia

From August 2003 to July 2004, specimens of the bivalve Venus verrucosa (L.) were collected monthly in the channel connecting the lagoon of Bizerte (Tunisia) to the Mediterranean Sea. During the winter, 4% of the specimens had tiny perforations on the outer and inner faces of the valves; the perforations were connected to an intra-valve network of galleries, caused by 10-12 mm Sipunculoidea. Of specimens collected in February-March, 4% were infested with the lithophagous bivalve, Gastrochaena dubia, that lived within a cavity in the V. verrucosa valves. The cavity communicated to the outside through a calcareous tube developed by the G. dubia near the exit of the V. verrucosa siphons, ndicating parasitism that can cause progressive perforation of the valve and lead to the death of the host

Inversion of noisy Radon transform by SVD based needlet

A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in $L^p$ ($1\le p\le \infty$) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed

Saint-Claude – Les Prés de Valfin

Les fouilles et recherches concernent l’ancienne commune de Valfin autrefois réputée pour ses chaufourniers, dont la famille Bourgeat qui en compta plusieurs générations. Les vestiges du four des « Prés de Valfin » sont situés sur la commune de Saint-Claude. Le four repose sur les marno-calcaires de l’Argovien (étage Jurassique supérieur) et se signale dans la topographie par une butte. Il consiste en un anneau de terre marron avec gros blocs épars de calcaire délimitant une cuvette de 6 à 8 ..

Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding

In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive.The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$.We prove lower bounds on the minimax risk for estimation of the density $f\_{\beta}$ over Besov bodies where the loss is a power of the $L^p(\mathbb{S}^{d-1})$ norm for $1\le p\le \infty$. We show that a hard thresholding estimator based on a needlet expansion with data-driven thresholds achieves these lower bounds up to logarithmic factors