A simple test for monotonicity and monotonicity-related properties

About this event

We describe and examine a test for shape constraints, such as monotonicity, convexity (or both such properties simultaneously), or U-shape, in a nonparametric framework using partial sums empirical process. 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. In addition, we outline how the methodology can be extended to a framework when other covariates are present and no shape-related properties are imposed on them.