- bioMerieux,

- CEA Cadarache,

- CERIES,

- EDF R&D,

- Hemera,

- Valeo,

- Xerox Research Centre Europe.

- ExtremReg - Extremal Regression with Applications to Econometrics, Environment and Finance, 2019-23. 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.

- Vahinés, ANR MDCO (Masse de Données et Connaissances), 2008-12. This three-year project is called "Visualisation et analyse d'images hyperspectrales multidimensionnelles en Astrophysique" (VAHINES). It aims at developing physical as well as mathematical models, algorithms, and software able to deal efficiently with hyperspectral multi-angle data but also with any other kind of large hyperspectral dataset (astronomical or experimental). It involves the Observatoire de la Côte d'Azur (Nice), and several universities (Strasbourg I and Grenoble I). [link]

Figure 1. Left: Grain size of CO2 versus spectra projected on the first GSRIR axis (see Bernard-Michel et al. 2009a, 2009b). Right: Reconstructed map of grain size of CO2 on the Mars planet.

- Medup, ANR VMC (Vulnérabilité : Milieux et climats), 2008-12. This three-year project is called "Forecast and projection in climate scenario of Mediterranean intense events: Uncertainties and Propagation on environment" (MEDUP) and deals with the quantification and identification of sources of uncertainties associated with the forecast and climate projection for Mediterranean high-impact weather events. The propagation of these uncertainties on the environment is also considered, as well as how they may combine with the intrinsic uncertainties of the vulnerability and risk analysis methods. It involves Meteo-France and several universities (Paris VI, Grenoble I and Toulouse III). [link]

Figure 2. Map of the mean return-levels of daily rainfall(in mm) for a period of 10 years in the Cévennes-Vivarais area (see Gardes and Girard 2010)

- Movistar, ACI "masse de données" program, 2003-06. This three-year project involves team Lear from Inria, SMS from University Joseph Fourier and Heudiasyc from UTC, Compiegne. The project aimed at investigating visual and statistical models for image recognition and description and learning techniques for the management of large image databases.