Semi-Parametric Models for Extremes In collaboration with Dr. Ilaria Prosdocimi, Centre for Ecology & Hydrology

While much effort in the development of statistical methods aims at characterising some properties of the central tendency of the distribution of a process, Extreme Values statistics aims at characterising the tail of a distribution. Extreme Values methods are used in a number of applications for which reliable estimates of the frequency of rare events are needed, for example finance (e.g., frequency of excessively large losses) or environmental sciences (e.g., the frequency of the over-topping of a dam or of a drought). Extreme Value models are typically motivated by some asymptotic laws which give an approximate distribution for the maxima of weakly long-range dependent series (see Coles (2001) for an introduction). It is often the case that rather than simply studying the behaviour of the process of interest Y, the conditional process (Y |X) might be of interest, with X a set of covariates. For example, if Y denotes the process describing high flows at a gauging station on a river, it could be of interest to study how Y changes with respect to, for example, the annual rainfall totals and the annual temperature. In particular, it would be of interest to allow the shape of the relationship between the process Y and the covariates X to be determined by the data at hand using non-parametric regression methods, such as penalized regressio