Inference in non parametric hidden Markov models
In this talk, I will review recent results on hidden Markov models with finite state space and non parametric modeling of the emission distributions. I will explain how identifiability can be obtained from the distribution of 2 consecutive observations when the emission distributions are translated from an unknown one, and from 3 consecutive observations in the general situation. I will show generic methods to build non parametric adaptive estimators and solve the inverse problem.
Higher order elicitability
Elicitability of a statistical functional means that it can be obtained as the
minimizer of an expected loss function. Prime examples of elicitable functionals are
the mean or quantiles of a random variable. Elicitability is a useful property for
model selection, generalized regression, forecast comparison, and forecast ranking.
Independently, Weber (2006, Mathematical Finance) and Gneiting (2011, JASA)
have shown that expected shortfall (ES), an important risk measure in banking and
finance, is not elicitable. However, it turns out that ES is jointly elicitable with a
certain quantile, that is, it is elicitable of second order.
In this talk, we present our results on higher order elicitability of ES and some
other functionals, and we provide characterizations of the associated classes of consistent
scoring functions. We illustrate the usefulness of scoring functions for backtesting
and model selection.
Joint work with: Tobias Fissler, Tilmann Gneiting, Alexander Jordan, Fabian
Krüger, Natalia Nolde