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arXiv · 1611.09744

Optimal adaptive estimation of linear functionals under sparsity

Olivier Collier·Laëtitia Comminges·Alexandre B. Tsybakov·Nicolas Verzélen
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Abstract

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. We suggest an estimator that achieves the optimal adaptive rate when both s and sigma^2 are unknown.

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Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov, Nicolas Verzélen. 2016-11-29. Optimal adaptive estimation of linear functionals under sparsity. https://arxiv.org/abs/1611.09744

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