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.
Keywords: Functional data analysis; Functional linear regression; Functional partial least squares;
Locally sparse; Bayesian analysis