3 papers
math.ST2019
Optimal solutions to the isotonic regression problem
Alexander I. Jordan, Anja Mühlemann, Johanna F. Ziegel
In general, the solution to a regression problem is the minimizer of a given loss criterion, and depends on the specified loss function. The nonparametric isotonic regression probl…
q-fin.RM2017
Murphy Diagrams: Forecast Evaluation of Expected Shortfall
Johanna F. Ziegel, Fabian Krüger, Alexander Jordan +1
Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to eva…
math.ST2015
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…