Statistique multidimensionnelle

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This research project is concerned with several areas of the statistical sciences, namely geometric statistics, survey sampling, copula modeling and capture-recapture experiments. It proposes to undertake the theoretical investigation, and the practical implementation, of new statistical models in response to modern challenges in data analysis. In biomechanics, rigid body motion data, consisting of rotation translation pairs are routinely collected to estimate the geometric characteristics of human joints. To make a better use of these data, statistical models will be developed for their analysis. In ecology it is now possible to record simultaneously the movement of an animal, and important features of its environment. This project will develop multivariate circular regression models to investigate how the direction of movement of an animal is influenced by the direction of features of its environement, such as its den or a patch rich in nutriment. In survey sampling copulas will be used to construct new flexible methods for estimating small area characteristics of a population. Methods for improving the estimation of the size of hard to reach populations in a capture-recapture experiment will also be investigated.