Local modeling for multivariate extremes and survival analysis

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The general objective of the proposed research program is to use and adapt local modeling methods in various class of non-parametric models. Theoretical and practical aspects of the obtained estimators will be investigated. In particular, we shall focus on the following estimation problems: 1. Extreme values related problems: In many applied problems, one needs to quantify the asymptotic dependence structure of multivariate data in order to estimate probabilities of associated rare sets. Our aim in this project is to investigate local modeling techniques when applied to the estimation of copulas, dependence functions, multivariate tail dependence measures, conditional probabilities associated to a random vector whose components are not necessarily jointly extreme. We also intend to use tail dependence measures and classical correlation coefficients to test independence of multivariate extremes. 2. Survival analysis: Analysis of time-to-event data is a problem frequently faced in various fields: medicine, public health, epidemiology, engineering, etc. There is a huge literature on this subject. Our scope for this project is to investigate local modeling for survival functions, regression, mean residual life functions, regression quantiles and various risk measures when : a) the lifetime and the censoring (or truncating) time are univariate dependent variables. or b) the observed lifetimes are bivariate (or multivariate) variables with unique or different censoring variables. 3. Item Response Theory and Equipercentile Equating are two different topics that we intend to investigate by using local fitting. They are related to Health Quality of Life, questionnaires and instruments used in health science.