14:00 – 15:00 Davy Paindaveine
Title: Hypothesis testing on high-dimensional spheres: an asymptotic approach
Abstract: Hypothesis testing in high dimensions has been a most active research topics in the last decades. Both theoretical and practical considerations make it natural to restrict to sign tests, that is, to tests that uses observations only through their directions from a given center. This obviously maps the original Euclidean problem to a spherical one, still in high dimensions. With this motivation in mind, we tackle two testing problems on high-dimensional spheres, both under a symmetry assumption that specifies that the distribution at hand is invariant under rotations with respect to a given axis. More precisely, we consider the problem of testing the null hypothesis of uniformity (“detecting the signal”) and the problem of testing the null hypothesis that the symmetry axis coincides with a given direction (“learning the signal direction”). We solve both problems by exploiting Le Cam’s asymptotic theory of statistical experiments, in a double- or triple-asymptotic framework. Interestingly, contiguity rates depend in a subtle way on how well the parameters involved are identified as well as on a possible further antipodally-symmetric nature of the distribution. In many cases, strong optimality results are obtained from local asymptotic normality. When this cannot be achieved, it is still possible to establish minimax rate optimality.
15:30 – 16:30 Alessandra Luati
Title: Dynamic models for multiple quantiles.
Abstract: We discuss recent developments on models for dynamic multiple quantiles. The baseline semiparametric model introduced by Catania and Luati (2022), based on quantile spacings and score-type updates, is reviewed and extended to account for: heterogeneous tail behaviour, cross tail effects, exogenous variables. The extensions result in a flexible class of models ensuring that quantiles do not cross in finite samples and that extreme quantiles are estimated based on information coming from all the regions of the underlying conditional distribution.
M-estimation is carried out and asymptotic properties of the estimators are discussed. We provide examples and illustrations on financial and macroeconomic variables.
Based on joint works with Leopoldo Catania (Aarhus University)
Refreshments available between 15:00 – 15:30