TY  - JOUR
A1  - Carpentier, Alexandra
A1  - Nickl, Richard
T1  - On signal detection and confidence sets for low rank inference problems
T2  - Electronic journal of statistics
N2  - We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal.
KW  - Low rank matrices
KW  - confidence sets
KW  - signal detection
KW  - nuclear norm
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/39269
SN  - 1935-7524
VL  - 9
IS  - 2
SP  - 2675
EP  - 2688
PB  - Institute of Mathematical Statistics
CY  - Cleveland
ER  -