| Abstract [eng] |
Functional Data Analysis refer to the analysis of information on functions or curves defined on some interval, which abbreviated as “FDA”. This involves thinking of the observed data as functions or curves rather than a set of data points. The aim of this thesis is to investigate some FDA methodologies, starting with the very first step of constructing the functional form of the sample curves from their discrete data points. The study includes one of the most popular techniques of which is Functional Principal Components Analysis(fPCA). FPCA is a popular and useful tool for dimension reduction. In addition, a Functional Linear Regression Model is constructed. The discrete observed data points for each involved variables are smoothing by Fourier Basis and B-spline Basis, roughness penalty used to control the degree of the smoothness, smoothing parameter set by generalized cross-validation (GCV). Finally,the functions of R2 and F-ratio were computed for the goodness-of-fit of functional linear model. Each of the aforementioned Functional Data Analysis methodologies applies to a real climate data set. |
