Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Collier, Olivier"'
Autor:
Carpentier, Alexandra, Collier, Olivier, Comminges, Laetitia, Tsybakov, Alexandre B., Wang, Yuhao
We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternativ
Externí odkaz:
http://arxiv.org/abs/2010.13679
Autor:
Collier, Olivier, Comminges, Laëtitia
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 generalize the results of (Collier et al., 2017, 2019) to a very large class
Externí odkaz:
http://arxiv.org/abs/1908.11070
We study the problem of estimation of the value N_gamma(\theta) = sum(i=1)^d |\theta_i|^gamma for 0 < gamma <= 1 based on the observations y_i = \theta_i + \epsilon\xi_i, i = 1,...,d, where \theta = (\theta_1,...,\theta_d) are unknown parameters, \ep
Externí odkaz:
http://arxiv.org/abs/1805.10791
Autor:
Carpentier, Alexandra, Collier, Olivier, Comminges, Laëtitia, Tsybakov, Alexandre B., Wang, Yuhao
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 that, in Gaussian linear regression model with p < n, where p is the dim
Externí odkaz:
http://arxiv.org/abs/1804.06494
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 of adaptive estimation when adaptation is considered with respect to
Externí odkaz:
http://arxiv.org/abs/1802.04230
Autor:
Collier, Olivier, Dalalyan, Arnak S.
We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of these means ar
Externí odkaz:
http://arxiv.org/abs/1712.05495
Autor:
Collier, Olivier, Dalalyan, Arnak
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 intensity. We are interested in estimating the sum of the n unknown intensity
Externí odkaz:
http://arxiv.org/abs/1712.01775
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a non-asymptotic rate
Externí odkaz:
http://arxiv.org/abs/1611.09744
Autor:
Collier, Olivier
De nombreuses applications, en vision par ordinateur ou en médecine notamment,ont pour but d'identifier des similarités entre plusieurs images ou signaux. On peut alors détecter des objets, les suivre, ou recouper des prises de vue. Dans tous les
Externí odkaz:
http://www.theses.fr/2013PEST1080/document
For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main object of inter
Externí odkaz:
http://arxiv.org/abs/1502.00665