A new nonparametric procedure for testing monotonicity of a regression mean is proposed. The test is shown to have prescribed asymptotic level and good asymptotic power. It is based on the supremum distance from an empirical process to its least concave majorant and is very easily implementable....

The least squares estimator of a discrete distribution under the constraint of convexity is introduced. Its existence and uniqueness are shown and consistency and rate of convergence are established. Moreover it is shown that it always outperforms the classical empirical estimator in terms of...

In this article, we develop a test for the null hypothesis that a real-valued function belongs to a given parametric set against the non-parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone...

Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of "maximizing the sharpness of the predictive...

In this paper, we describe two computational methods for calculating the cumulative distribution function and the upper quantiles of the maximal difference between a Brownian bridge and its concave majorant. The first method has two different variants that are both based on a Monte Carlo...