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Estimation of the -norm and testing in sparse linear regression with unknown variance
Alexandra Carpentier, Olivier Collier, Laetitia Comminges +2
We consider the related problems of estimating the -norm and the squared -norm in sparse linear regression with unknown variance, as well as the problem of testing the hy…
Minimax optimal estimators for general additive functional estimation
Olivier Collier, Laëtitia Comminges
In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we general…
On estimation of nonsmooth functionals of sparse normal means
Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov
We study the problem of estimation of the value N_gamma(θ) = sum(i=1)^d |θ_i|^gamma for 0 < gamma <= 1 based on the observations y_i = θ_i + εξ_i, i = 1,...,d, where θ= (θ_1,...,θ_…
Minimax rate of testing in sparse linear regression
Alexandra Carpentier, Olivier Collier, Laëtitia Comminges +2
We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show th…
Adaptive robust estimation in sparse vector model
Laëtitia Comminges, Olivier Collier, Mohamed Ndaoud +1
For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates…
Estimating linear functionals of a sparse family of Poisson means
Olivier Collier, Arnak Dalalyan
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensi…