Adaptive confidence bands in the nonparametric fixed design regression   model
  In this note, we consider the problem of existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl (2011) to the present case. In the course of the proof, we show that sup-norm adaptive estimators exist as well in regression. 
Pierre-Yves Mass\'e and William Meiniel
math.ST stat.TH