ABSTRACT
This chapter covers a mix of topics including splines, functional data, extreme values and density estimation. Being associated with continuous time monitoring processes, functional data are usually smooth curves or surfaces and are often treated as realizations of underlying random functions. The basic philosophy of functional data is to consider the observed curves as single entities, rather than only as a sequence of individual observations. Comprehensive surveys of statistical techniques for analyzing functional data can be found in Ramsay and Silverman and Ferraty and Vieu. Goldsmith study Diffusion Tensor Imaging (DTI) metrics of multiple sclerosis (MS) patients over multiple clinical visits. The data consist of 100 subjects, aged between 21 and 70 years at first visit. The number of visits per subject ranges from 2 to 8, and a total of 340 visits were recorded. Most statistical modeling is concerned with the mean response but in some applications, the extreme values of the response are the main interest.
