TY  - JOUR
A1  - Blanchard, Gilles
A1  - Carpentier, Alexandra
A1  - Gutzeit, Maurilio
T1  - Minimax Euclidean separation rates for testing convex hypotheses in R-d
JF  - Electronic journal of statistics
N2  - We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a closed convex subset C of R-d. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension d and variance 1/n giving rise to the minimax separation rate. In this paper we discuss lower and upper bounds on this rate for different smooth and non-smooth choices for C.
KW  - Minimax hypothesis testing
KW  - Gaussian sequence model
KW  - nonasymptotic minimax separation rate
Y1  - 2018
U6  - https://doi.org/10.1214/18-EJS1472
SN  - 1935-7524
VL  - 12
IS  - 2
SP  - 3713
EP  - 3735
PB  - Institute of Mathematical Statistics
CY  - Cleveland
ER  -