Béatrice Laurent

A Dvoretzky-Kiefer-Wolfowitz type inequality for the Kaplan-Meier estimator

Abstract We prove a new exponential inequality for the Kaplan–Meier estimator of a distribution function in a right censored data model. This inequality is of the same type as the Dvoretzky–Kiefer–Wolfowitz inequality for the empirical distribution function in the non-censored case. Our approach is based on Duhamel equation which allows to use empirical process theory.

Bacterial translational regulations: high diversity between all mRNAs and major role in gene expression

BackgroundIn bacteria, the weak correlations at the genome scale between mRNA and protein levels suggest that not all mRNAs are translated with the same efficiency. To experimentally explore mRNA translational level regulation at the systemic level, the detailed translational status (translatome) of all mRNAs was measured in the model bacterium Lactococcus lactis in exponential phase growth.ResultsResults demonstrated that only part of the entire population of each mRNA species was engaged in translation. For transcripts involved in translation, the polysome size reached a maximum of 18 ribosomes. The fraction of mRNA engaged in translation (ribosome occupancy) and ribosome density were not constant for all genes. This high degree of variability was analyzed by bioinformatics and statistical modeling in order to identify general rules of translational regulation. For most of the genes, the ribosome density was lower than the maximum value revealing major control of translation by initiation. Gene function was a major translational regulatory determinant. Both ribosome occupancy and ribosome density were particularly high for transcriptional regulators, demonstrating the positive role of translational regulation in the coordination of transcriptional networks. mRNA stability was a negative regulatory factor of ribosome occupancy and ribosome density, suggesting antagonistic regulation of translation and mRNA stability. Furthermore, ribosome occupancy was identified as a key component of intracellular protein levels underlining the importance of translational regulation.ConclusionsWe have determined, for the first time in a bacterium, the detailed translational status for all mRNAs present in the cell. We have demonstrated experimentally the high diversity of translational states allowing individual gene differentiation and the importance of translation-level regulation in the complex process linking gene expression to protein synthesis.

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

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.

Non asymptotic minimax rates of testing in signal detection with heterogeneous variances

The aim of this paper is to establish non-asymptotic minimax rates of testing for goodness-of-fit hypotheses in a heteroscedastic setting. More precisely, we deal with sequences

Adaptive goodness-of-fit tests in a density model

(Y_j)_{j\in J}

Adaptive tests of homogeneity for a Poisson process

of independent Gaussian random variables, having mean

Adaptive estimation of linear functionals by model selection

(\theta_j)_{j\in J}

Linear covariance models to examine the determinants of protein levels in Lactococcus lactis

and variance

The two-sample problem for Poisson processes: adaptive tests with a non-asymptotic wild bootstrap approach

(\sigma_j)_{j\in J}

Signal detection for inverse problems in a multidimensional framework

. The set