Before revision: We describe and examine a test for  shape constraints, such as monotonicity, convexity (or both simultaneously) , U-shape, S-shape and others, in a nonparametric framework using partial sums empirical processes.
After revision: We describe and examine a test for shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity , U-shape, S-shape and others, in a nonparametric framework using partial sums empirical processes.