26 citations · 41 across the 6 of their papers we have counts for
9 papers
On certain Gram matrices and their associated series
Werner Ehm
We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n…
Forecast dominance testing via sign randomization
Werner Ehm, Fabian Krüger
We propose randomization tests of whether forecast 1 outperforms forecast 2 across a class of scoring functions. This hypothesis is of applied interest: While the prediction contex…
Geometric-optical illusions and Riemannian geometry
Werner Ehm, Jiri Wackermann
Geometric-optical illusions (GOI) are a subclass of a vast variety of visual illusions. A special class of GOIs originates from the superposition of a simple geometric figure ("tar…
Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings
Werner Ehm, Tilmann Gneiting, Alexander Jordan +1
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive…
Modeling geometric-optical illusions: A variational approach
Werner Ehm, Jiri Wackermann
Visual distortions of perceived lengths, angles, or forms, are generally known as "geometric-optical illusions" (GOI). In the present paper we focus on a class of GOIs where the di…
Unbiased risk estimation and scoring rules
Werner Ehm
Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general diverg…