FROMONT , Magalie

Let (X,Y) be a X x {0,1}-valued random pair and consider a sample (X-1, Y-1),..., (X-n, Y-n.) drawn from the distribution of (X, Y). We aim at constructing from this sample a classifier that is a function which would predict the value of Y from the observation of X. The special case where X is a functional space is of particular interest due to...

Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The corresponding critical values are constructed from a non-asymptotic wild bootstrap approach, leading to level...

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov bodies. Surprisingly, the obtained lower bounds over weak Besov bodies coincide with the minimax estimation...

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov bodies. Surprisingly, the obtained lower bounds over weak Besov bodies coincide with the minimax estimation...

Starting from a parallel between some minimax adaptive tests of a single null hypothesis, based on aggregation approaches, and some tests of multiple hypotheses, we propose a new second kind error-related evaluation criterion, as the core of an emergent minimax theory for multiple tests. Aggregation-based tests are justified through their first...

We investigate several distribution-free dependence detection procedures, all based on a shuffling of the trials, from a statistical point of view. The mathematical justification of such procedures lies in the bootstrap principle and its approximation properties. In particular, we show that such a shuffling has mainly to be done on centered...

Considering either two independent i.i.d. samples, or two independent samples generated from a heteroscedastic regression model, or two independent Poisson processes, we address the question of testing equality of their respective distributions. We first propose single testing procedures based on a general symmetric kernel. The corresponding...

Given a times series Y in R n , with a piece-wise contant mean and independent components, the twin problems of change-point detection and change-point localization respectively amount to detecting the existence of times where the mean varies and estimating the positions of those change-points. In this work, we tightly characterize optimal...

Considering either two independent i.i.d. samples, or two independent samples generated from a heteroscedastic regression model, or two independent Poisson processes, we address the question of testing equality of their respective distributions. We first propose single testing procedures based on a general symmetric kernel. The corresponding...

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general $U$-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation...