Fetching the paper…

Reading the bibliography…

2016

Optimal adaptive estimation of linear functionals under sparsity

Collier, Olivier, Comminges, Laëtitia, Tsybakov, Alexandre B. et al.

Original
PDF
Post on X

Understand

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 of convergence that differs from the minimax rate at most by a logarithmic factor.
We also show that this optimal adaptive rate cannot be improved when s is unknown.
Furthermore, we address the issue of simultaneous adaptation to s and to the variance sigma^2 of the noise.

Optimal adaptive estimation of linear functionals under sparsity · Around

Built on

Nonparametric estimation of the value of a linear functional in Gaussian white noise
1984
Earlier work this paper cites.
Probability in Banach Spaces
1991
Earlier work this paper cites.
Limit Theorems of Probability Theory
1995
Earlier work this paper cites.
Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
1998
Earlier work this paper cites.

Similar

Minimax estimation of linear functionals over nonconvex parameter spaces
2004
Cited alongside, same era.
The method of risk envelopes in the estimation of linear functionals
2004
Cited alongside, same era.
Math. Methods Statist
2004
Cited alongside, same era.
On adaptive estimation of linear functionals
2005
Cited alongside, same era.

Then

Adaptive estimation of linear functionals by model selection
2008
Later among the works it cites.
Introduction to Nonparameric Estimation
2009
Later among the works it cites.
Minimax risks for sparse regressions: Ultra-high dimensional phenomenons
2012
Later among the works it cites.
Ann. Statist
2017
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…