English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a new method for estimating the risk of an arbitrary estimator ofthe mean vector in the classical normal means problem. The key idea is togenerate two auxiliary data vectors, by adding carefully constructed normalnoise vectors to the original data. We then train the estimator of interest onthe first auxiliary vector and test it on the second. In order to stabilizerisk estimate, we average this procedure over multiple draws of the syntheticnoise. A key aspect of this coupled bootstrap approach is that it delivers anunbiased estimate of risk under no assumptions on the estimator of the meanvector, albeit for a slightly "harder" version of the original problem, wherethe noise variance is inflated. We show that, under the assumptions requiredfor Stein's unbiased risk estimator (SURE), a limiting version of thisestimator recovers SURE exactly. We also analyze a bias-variance decompositionof the error of our risk estimator, to elucidate the effects of the variance ofthe auxiliary noise and the number of bootstrap samples on the accuracy of theestimator. Lastly, we demonstrate that our coupled bootstrap risk estimatorperforms quite favorably in simulated experiments and in a denoising example.

Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques