Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unbiased Risk Estimation in the Normal Means Problem via Coupled
  Bootstrap Techniques   We study a new method for estimating the risk of an arbitrary estimator of
the mean vector in the classical normal means problem. The key idea is to
generate two auxiliary data vectors, by adding two carefully constructed normal
noise vectors to the original data vector. We then train the estimator of
interest on the first auxiliary data vector and test it on the second. In order
to stabilize the estimate of risk, we average this procedure over multiple
draws of the synthetic noise. A key aspect of this coupled bootstrap approach
is that it delivers an unbiased estimate of risk under no assumptions on the
estimator of the mean vector, albeit for a slightly "harder" version of the
original normal means problem, where the noise variance is inflated. We show
that, under the assumptions required for Stein's unbiased risk estimator
(SURE), a limiting version of the coupled bootstrap estimator recovers SURE
exactly (with an infinitesimal auxiliary noise variance and infinite bootstrap
samples). We also analyze a bias-variance decomposition of the error of our
risk estimator, to elucidate the effects of the variance of the auxiliary noise
and the number of bootstrap samples on the accuracy of the risk estimator.
Lastly, we demonstrate that our coupled bootstrap risk estimator performs quite
favorably in simulated experiments and in an image denoising example.

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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: hep-ex