Statistical inference for flexible modelling of functional data.

The analysis of functional data has seen an increasing interest in the last two decades. Functional data are encountered in many fields, such as in seismology, in medical applications, in biology or in food safety to name just some examples. In each case (in principle) a curve is observed, as opposed to a single number or a vector in traditional regression; often measurements are taken over time. The main focus in the literature so far has been on estimating, from observed functional data, a functional mean pattern. Apart from studying a functional mean curve, there is also the important issue to measure the possible functional variation (heterogeneity) present in functional data. We propose to study the joint estimation of the functional mean and variation via flexible models using B-splines. In addition, simultaneous confidence bands for both the mean and the variation curves will be constructed. A flexible model for the dependencies between two random curves will be obtained via a study of copulas in the functional context.