Extremal Regression with Applications to Econometrics, Environment and Finance (ExtremReg)
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, which is the reason 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. 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.
Our research in the second and third items is also interdisciplinary in nature, involving statistics and risk management in environment, actuarial science and finance. Of special interest in our project are two concrete applications in geology and meteorology. Estimating extreme seismic magnitudes and extreme rainfalls, as well as the corresponding losses, conditional on the geographical location (and other spatial characteristics) is crutial to guide future policy towards risk protection. In order to guarantee a reactive and prudent differentiation of tail risk geographically, it is important to incorporate the random spatial nature of covariates and the temporal dimension into the extreme-value estimation procedures.
Project : 2019 – 2023