The project concentrates around three themes that are central to the area of modern extreme value statistics. First, we contribute to the expanding literature on non regular regression models where the observation errors are assumed to be one-sided and the regression function describes some frontier or boundary curve. This is motivated from abundant applications especially in production econometrics. The development of mathematical properties under these frontier models is, however, often a lot harder than under the standard regression models. In particular, classical regularity conditions are violated, hence why these models are typically referred to as non regular. Our project tries to solve these difficulties in different directions, namely polynomial spline fitting under shape constraints, estimation from noisy data using inverse problems, and estimation of locally stationary, one-sided autoregressive processes.
Second, we further investigate the recent extreme value theory built on the use of asymmetric least squares instead of order statistics. We focus on two least squares analogues of quantiles, called expectiles and extremiles. These concepts have gained increasing interest in risk management. While the extreme value properties of expectiles are well developed, much less is known about tail extremiles. For this reason, we aim to establish weighted approximations of the tail empirical extremile process, valid under mixing conditions. This part of the project is also dedicated to statistical expectile depth and multiple-output expectile regression methods.
Finally, we explore the important problem of estimating conditional and joint extremes in high dimension, which is still in full development.
The objectives of this part of the project are twofold. On the one hand, we will provide a general toolbox for estimating tail regression expectiles and extremiles in high dimension. On the other hand, we will discuss dimension reduction techniques when modeling the joint extremes of simultaneous time series.
Monsieur Abdelaati Daouia (FONDATION JEAN JACQUES LAFFONT)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
IRMA_UNISTRA Institut de recherche mathématique avancée (UMR 7501)
INRIA GRA Centre de Recherche Inria Grenoble - Rhône-Alpes
TSE FONDATION JEAN JACQUES LAFFONT
Université Libre de Bruxelles / European Center for Advanced Research in Economics and Statistics (ECARES)
Seoul National University / Department of Statistics
Technische Universität Braunschweig / Institut für Mathematische Stochastik
ENSAI ENSAI Rennes & CREST
Help of the ANR 159,000 euros
Beginning and duration of the scientific project: September 2019 - 48 Months