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