We investigate whether in a distributed setting, adaptive estimation of smooth function at the optimal rate is possible under minimal communication. It turns out that answer depends on risk considered and number servers over which procedure distributed. show for $L\_\infty$-risk, adaptively obtaining rates communication not possible. For $L\_2$-risk, it range regularities relation between local...

Characterizing and analyzing a system often requires learning an unknown function, such as the response of or profile field. The standard approach is to opportunely sample function at fiducial points then interpolate. When quantity interest embodied in physical objects accessible with quantum-enhanced measurements, it becomes relevant investigate how transfer this advantage from individual samp...

The estimation of a log-concave density on Rd represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to global loss functions, and adopt a minimax approach. We first show that no statistical procedure based on a sample of size n can estimate a log-concave density with res...