We show that the supremum distance between the cumulative distribution of the convex LSE and an arbitrary distribution function F with a convex pmf on N is at most twice the supremum distance between the empirical distribution function and F.

The computation of robust regression estimates often relies on minimization of a convex functional on a convex set. In this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization-minimization...

The computation of robust regression estimates often relies on minimization of a convex functional on a convex set. In this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization-minimization...

The fact that a k-monotone density can be defined by means of a mixing distribution makes its estimation feasible within the framework of mixture models. It turns the problem naturally into estimating a mixing distribution, nonparametrically. This paper studies the least squares approach to...

A set of ellipses, with given semi-major and semi-minor axes, is to be cut from a rectangular design plate, while minimizing the area of the design rectangle. The design plate is subject to lower and upper bounds of its widths and lengths; the ellipses are free of any orientation restrictions....

The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we...

The classes of monotone or convex (and necessarily monotone) densities on inline image can be viewed as special cases of the classes of k-monotone densities on inline image. These classes bridge the gap between the classes of monotone (1-monotone) and convex decreasing (2-monotone) densities for...