View Submission - CFE

A0216
**Title: **Elicitability: The quest of comparing risk measure estimates in a meaningful way
**Authors: **Tobias Fissler - Imperial College London (United Kingdom) **[presenting]**

Johanna F Ziegel - University of Bern (Switzerland)

Tilmann Gneiting - Heidelberg Institute for Theoretical Studies (Germany)

**Abstract: **In statistical decision-theory, it is common practice to compare competing point forecasts for unknown future events in terms of loss functions. That is, a forecaster issuing the forecast $x$ is assigned the \textit{loss} $L(x,y)$ if $y$ materializes. Considering forecasts for a certain statistical functional such as the mean, the median, or a risk measure, it is crucial that the loss function used is incentive compatible in the sense that the correctly specified forecast for the functional is the unique minimizer of the expected loss. If a functional possesses such an incentive compatible loss function, it is called elicitable, opening the way to meaningful forecast comparison, but also to M-estimation and regression. Many functionals such as expectiles or quantiles are elicitable, whereas other important quantities such as the variance or Expected Shortfall fail to be elicitable. Nevertheless, they can be components of elicitable vector-valued functionals, in particular, both mean and variance, as well as Value-at-Risk and Expected Shortfall are \textit{jointly} elicitable. The latter result opens the possibility to \textit{comparative} backtests aiming at model selection rather than model validation which turns out to be beneficial in the context of quantitative risk management.

Johanna F Ziegel - University of Bern (Switzerland)

Tilmann Gneiting - Heidelberg Institute for Theoretical Studies (Germany)