Limit theorems of functional data analysis with some applications

Lajos Horváth and Ron Reeder

University of Utah

Functional data analysis is concerned with observations which are viewed as functions defined over some set T . It can be temperature at a given location, stock prices, exchange rates, components of a magnetic field, growth curves and so on. Clearly, due to finite resolution, the values of the curve are available at a finite grid of points but due to the density of the grid and the physical interpretation of the curve, it is assumed that the observation is defined on T . We describe the basic principles of functional data analysis, including projections, the choice and estimation of the directions of the projections. We provide several examples for the applicability of the functional interpretation of the data, including the comparison of the mean curves of two populations, volatility models and functional regression.