## Bernoulli

• Bernoulli
• Volume 24, Number 4A (2018), 2429-2460.

### Adaptive confidence sets for matrix completion

#### 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.

#### Article information

Source
Bernoulli, Volume 24, Number 4A (2018), 2429-2460.

Dates
Revised: January 2017
First available in Project Euclid: 26 March 2018

https://projecteuclid.org/euclid.bj/1522051214

Digital Object Identifier
doi:10.3150/17-BEJ933

Mathematical Reviews number (MathSciNet)
MR3779691

Zentralblatt MATH identifier
06853254

#### Citation

Carpentier, Alexandra; Klopp, Olga; Löffler, Matthias; Nickl, Richard. Adaptive confidence sets for matrix completion. Bernoulli 24 (2018), no. 4A, 2429--2460. doi:10.3150/17-BEJ933. https://projecteuclid.org/euclid.bj/1522051214

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