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OPTIMAL ADAPTIVE ESTIMATION OF LINEAR FUNCTIONALS UNDER SPARSITY
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DOI：10.1214/17-AOS1653.png)
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Abstract
En 中文
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta is an element of R-d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a nonasymptotic 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.
Keywords:
Nonasymptotic minimax estimation
adaptive estimation
linear functional
sparsity
unknown noise variance
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