  We describe and examine a test for a general class of shape constraints, such
as constraints on the signs of derivatives, U-(S-)shape, symmetry,
quasi-convexity, log-convexity, $r$-convexity, among others, in a nonparametric
framework using partial sums empirical processes. We show that, after a
suitable transformation, its asymptotic distribution is a functional of the
standard Brownian motion, so that critical values are available. However, due
to the possible poor approximation of the asymptotic critical values to the
finite sample ones, we also describe a valid bootstrap algorithm.
