Noisy recovery from random linear observations: Sharp minimax rates under elliptical constraints
随机线性观测下的含噪恢复：椭球约束下的精确极小极大速率
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear operator; an important special case is random design regression. We derive sharp rates of estimation for arbitrary compact elliptical parameter sets and demonstrate how they depend on the distribution of the random linear operator. Our…