Sylvie Huet

Gaussian model selection with an unknown variance

Let Y be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean μ of Y by model selection. More precisely, we start with a collection

High-dimensional regression with unknown variance

\mathcal{S}=\{S_{m},m\in\mathcal{M}\}

Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function

of linear subspaces of ℝn and associate to each of these the least-squares estimator of μ on Sm. Then, we use a data driven penalized criterion in order to select one estimator among these. Our first objective is to analyze the performance of estimators associated to classical criteria such as FPE, AIC, BIC and AMDL. Our second objective is to propose better penalties that are versatile enough to take into account both the complexity of the collection

Yeast Proteome Variations Reveal Different Adaptive Responses to Grape Must Fermentation

\mathcal{S}

Least-squares estimation of a convex discrete distribution

and the sample size. Then we apply those to solve various statistical problems such as variable selection, change point detections and signal estimation among others. Our results are based on a nonasymptotic risk bound with respect to the Euclidean loss for the selected estimator. Some analogous results are also established for the Kullback loss.

Seed Spillage from Grain Trailers on Road Verges during Oilseed Rape Harvest: An Experimental Survey

We review recent results for high-dimensional sparse linear re- gression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation- sparsity. The emphasis is put on nonasymptotic analyses and feasible pro- cedures. In addition, a small numerical study compares the practical perfor- mance of three schemes for tuning the lasso estimator and some references are collected for some more general models, including multivariate regres- sion and nonparametric regression.

Hybridization within Saccharomyces Genus Results in Homoeostasis and Phenotypic Novelty in Winemaking Conditions

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in ℝn belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the tests achieve a prescribed power. In the functional regression model this general methodology is applied to test some qualitative hypotheses on the regression function. For example, we test that the regression function is positive, increasing, convex, or more generally, satisfies a differential inequality. Uniform separation rates over classes of smooth functions are established and a comparison with other results in the literature is provided. A simulation study evaluates some of the procedures for testing monotonicity.

Pharmacokinetic Analysis of Mizolastine in Healthy Young Volunteers After Single Oral and Intravenous Doses: Noncompartmental Approach and Compartmental Modeling

Saccharomyces cerevisiae and S. uvarum are two domesticated species of the Saccharomyces sensu stricto clade that diverged around 100 Ma after whole-genome duplication. Both have retained many duplicated genes associated with glucose fermentation and are characterized by the ability to achieve grape must fermentation. Nevertheless, these two species differ for many other traits, indicating that they underwent different evolutionary histories. To determine how the evolutionary histories of S. cerevisiae and S. uvarum are mirrored on the proteome, we analyzed the genetic variability of the proteomes of domesticated strains of these two species by quantitative mass spectrometry. Overall, 445 proteins were quantified. Massive variations of protein abundances were found, that clearly differentiated the two species. Abundance variations in specific metabolic pathways could be related to phenotypic traits known to discriminate the two species. In addition, proteins encoded by duplicated genes were shown to be differently recruited in each species. Comparing the strain differentiation based on the proteome variability to those based on the phenotypic and genetic variations further revealed that the strains of S. uvarum and some strains of S. cerevisiae displayed similar fermentative performances despite strong proteomic and genomic differences. Altogether, these results indicate that the ability of S. cerevisae and S. uvarum to complete grape must fermentation arose through different evolutionary roads, involving different metabolic pathways and duplicated genes.

Estimator selection in the Gaussian setting

The least squares estimator of a discrete distribution under the constraint of convexity is introduced. Its existence and uniqueness are shown and consistency and rate of convergence are established. Moreover it is shown that it always outperforms the classical empirical estimator in terms of the Euclidean distance. Results are given both in the well- and the mis-specified cases. The performance of the estimator is checked throughout a simulation study. An algorithm, based on the support reduction algorithm, is provided. Application to the estimation of species abundance distribution is discussed.

Assessing the Validity Domains of Graphical Gaussian Models in Order to Infer Relationships among Components of Complex Biological Systems

Context Anthropogenic vectors enhance the natural dispersal capacity of plant seeds significantly in terms of quantity and distance. Human-mediated seed dispersal (i.e. anthropochory) greatly increases the dispersal of crop species across agroecosystems. In the case of oilseed rape (OSR), spillage of seeds from grain trailers during harvest has never been quantified. Methods Our experimental approach involved establishing 85 seed trap-sites on the road verges of an agricultural area around the grain silo of Selommes (Loir-et-Cher, France). We recorded OSR spillage during harvest and applied a linear model to the data. Results The amount of seed spilled was related positively to the area of the OSR fields served by the road, whereas the amount of seed spilled decreased with other variables, such as distance from the trap-site to the verge of the road and to the nearest field. The distance to the grain silo, through local and regional effects, affected seed loss. Local effects from fields adjacent to the road resulted in a cumulative spillage on one-lane roads. On two-lane roads, spillage was nearly constant whatever the distance to the silo due to a mixture of these local effects and of grain trailers that joined the road from more distant fields. From the data, we predicted the number of seeds lost from grain trailers on one road verge in the study area. We predicted a total spillage of 2.05×106 seeds (±4.76×105) along the road length, which represented a mean of 404±94 seeds per m2. Conclusion Containment of OSR seeds will always be challenging. However, seed spillage could be reduced if grain trailers were covered and filled with less seed. Reducing distances travelled between fields and silos could also limit seed loss.