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November 2018 Adaptive confidence sets for matrix completion
Alexandra Carpentier, Olga Klopp, Matthias Löffler, Richard Nickl
Bernoulli 24(4A): 2429-2460 (November 2018). DOI: 10.3150/17-BEJ933

Abstract

In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.

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Alexandra Carpentier. Olga Klopp. Matthias Löffler. Richard Nickl. "Adaptive confidence sets for matrix completion." Bernoulli 24 (4A) 2429 - 2460, November 2018. https://doi.org/10.3150/17-BEJ933

Information

Received: 1 August 2016; Revised: 1 January 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853254
MathSciNet: MR3779691
Digital Object Identifier: 10.3150/17-BEJ933

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 4A • November 2018
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