Tobias Fissler: The Efficiency Gap
Parameter estimation via M- and Z-estimation is broadly considered to be equally powerful in semiparametric models for one-dimensional functionals. This is due to the fact that, under sufficient regularity conditions, there is a one-to-one relation between the corresponding objective functions – strictly consistent loss functions and oriented strict identification functions – via integration and differentiation. When dealing with multivariate functionals such as multiple moments, quantiles, or the pair (Value at Risk, Expected Shortfall), this one-to-one relation fails due to integrability conditions: Not every identification function possesses an antiderivative. The most important implication of this failure is an efficiency gap: The most efficient Z-estimator often outperforms the most efficient M-estimator, implying that he semiparametric efficiency bound cannot be attained by the M-estimator in these cases. We show that this phenomenon arises for pairs of quantiles at different levels and for the pair (Value at Risk, Expected Shortfall), and we illustrate the gap through extensive simulation studies.
This talk is based on joint ongoing work with Timo Dimitriadis (Heidelberg University) and Johanna Ziegel (University of Bern).
Jan Greve: Sparse modeling of factorial experiments with Bayesian finite mixtures
In experimental design, a common structure in data one often encounters involves multiple inputs purposely altered to different levels to efficiently study its relation to the resulting outputs. A factorial experiment refers to a specific setting where each input is constrained to have finitely many levels (either qualitative or quantitative) resulting in experimental units defined over finitely many combinations of these input levels. An experiment with this structure is not only common in natural sciences, but also known as conjoint analysis in marketing, and computational techniques in Machine Learning such as grid search can also be considered a variant of this practice. Our work aims at recovering a sparse probabilistic representation of experimental units from factorial experiment data by grouping together levels within each input so as to drastically reduce the dimension of the experimental design. While a work of similar nature in Bayesian paradigm was previously attempted by Nobile and Green (2000), their model failed to achieve one-to-one correspondence to data because of limited handing of identification of mixture models under the complicated dependence structure introduced through the factorial design. Our work based on methods developed by Frühwirth-Schnatter, Malsiner-Walli and Grün (2020) as well as on recent development in experimental design aims at resolving these identification problems. This ultimately allows for more concise inference on otherwise combinatorially increasing design space and also gives informative statistics to run follow-up experiments targeted at reducing the uncertainty in a specific group of experimental units.
Kory Johnson: " Estimating the reproduction number in the presence of superspreading"
Abstract: A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of COVID-19. In this technical report, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases. Accordingly, we employ a simple extension to models currently used in the literature to estimate the reproduction number and present a case-study of the progression of COVID-19 in Austria. Our models demonstrate that the estimation uncertainty of the reproduction number increases with superspreading.