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dc.contributor.authorKlopp, Olga
dc.subjectrecovery of the ranken
dc.subjectlow rank matrix estimationen
dc.subjectmatrix regressionen
dc.subjectMatrix completionen
dc.titleHigh dimensional matrix estimation with unknown variance of the noiseen
dc.typeDocument de travail / Working paper
dc.contributor.editoruniversityotherCentre de Recherche en Économie et Statistique (CREST) INSEE – École Nationale de la Statistique et de l'Administration Économique;France
dc.description.abstractenWe propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new method for estimating $A_0$ which does not rely on the knowledge or an estimation of the standard deviation of the noise $\sigma$. Our estimator achieves, up to a logarithmic factor, optimal rates of convergence under the Frobenius risk and, thus, has the same prediction performance as previously proposed estimators which rely on the knowledge of $\sigma$. Our method is based on the solution of a convex optimization problem which makes it computationally attractive.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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