Some new methods and models in functional data analysis

With new developments in modern technology, data are recorded continuously on a large scale over finer and finer grids. Such data push forward the development of functional data analysis (FDA), which analyzes information on curves or functions. Analyzing functional data is intrinsically an infinite-dimensional problem. Functional partial least squares method is a useful tool for dimension reduction. In this thesis, we propose a sparse version of the functional partial least squares method which is easy to interpret. Another problem of interest in FDA is the functional linear regression model, which extends the linear regression model to the functional context. We propose a new method to study the truncated functional linear regression model which assumes that the functional predictor does not influence the response when the time passes a certain cutoff point. Motivated by a recent study of the instantaneous in-game win probabilities for the National Rugby League, we develop novel FDA techniques to determine the distributions in a Bayesian model.