Title:
Loss Functions in Action
Abstract:
Loss functions are the ultimate tool in both regression and forecast comparison. Ideally, loss functions should reflect the actual costs of misspecified forecasts or regression models. However, often these costs are unknown or too difficult to model. Then, the goal is often given in terms of a statistical functional such as the mean, a quantile, or a risk measure of the observation. One reasonable requirement is that the loss function at hand rewards truthful forecasts in that the expected loss in minimised by the correctly specified forecast. Such loss functions are called strictly consistent for the respective functional. If the functional possesses a strictly consistent loss function, it is called elicitable.
In this talk, I will give an overview over the four important questions in that area:
i) Is the functional under consideration elicitable?
ii) If yes, how does the class of strictly consistent loss functions for a specific functional look like?
iii) Given the whole class of strictly consistent loss functions, what is a particularly appealing choice?
iv) What to do if a functional is not elicitable?
This talk is based on joint work with Johanna F. Ziegel.
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