Adaptive confidence sets in shape restricted regression

A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the set enjoys uniform coverage over all non-decreasing regression functions. Furthermore, diameter automatically adapts to unknown number pieces true parameter, sense that bounded from above by minimax risk class $k$-piecewise constant The a increasing function jumps least-squares estimate. similar where piecewise affine. Here, its affine function. an We explain how extend this technique non-convex proposing