My research highlights in 2013 Stéphane Girard

This short note lists my scientific results in 2013. Two main research topics are addressed: High dimensional statistical learning and Extreme-value analysis. 1 High dimensional statistical learning Copula provides a relevant tool to build multivariate probability laws, from fixed marginal distributions and required degree of dependence. From Sklar’s Theorem, the dependence properties of a continuous multivariate distribution can be entirely summarized, independently of its margins, by a copula. I proposed a new family of multivariate copulas adapted to high-dimensional problems. The family is built from a one-factor model [1, 2]. The estimation is performed using a moments method. Besides, I developped dimension reduction methods for high dimensional regression problems, see [3] for an application to the estimation of dominant physical parameters for leakage variability in 32nanometer CMOS. I also worked on the optimization of power consumption and user impact based on point process modeling of the request sequence. See [4] for an application to printers. 2 Extreme-value analysis The decay of the survival function is driven by a real parameter called the extreme-value index. When this parameter is positive, the survival function is said to be heavy-tailed. I focused on the situation where a covariate is recorded simultaneously the variable of interest. In this case, the extreme-value index and the extreme quantile depend on the covariate [5, 6]. It may be the case in hydrology for instance, see [7] for an application to the study of extreme rainfalls. The estimation of extreme risk measures is addressed in [8, 9, 10, 11, 12]. When this parameter is negative, the survival function vanishes above its right end point. The