Functional Data Analysis
Objectives
This course aims to provide an introduction to functional data analysis (FDA). The fundamental statistical tools for modeling and analyzing such data will be explored. This course introduces ideas and methodology in FDA as well as the use of software. Students will learn the idea of different methods and the related theory, and also the numerical and estimation routines to perform functional data analysis. Students will also have an opportunity to learn how to apply FDA to a wide array of application areas. The course will contain several examples where FDA techniques have clear advantage over classical multivariate techniques. Some recent development in FDA will also be discussed.
Course outline
Chapter 1. Introduction.
Chapter 2. Representing functional data and exploratory data analysis. Including: basic expansions, FPCA, derivatives, smoothing, packages.
Chapter 3. Basic elements of Hilbert space theory and random functions.
Chapter 4. Estimation and inference from a random sample. Including, estimation of functional principal component analysis (FPCA). Inference about the mean function.
Chapter 5. Functional Linear regression models. Including: Functional linear regression models with scalar and functional response variable (function-on-scalar, scalar-on-function and function-on-function
models).
Chapter 6. Functional generalized linear models
Chapter 7. (depending on the available time) Functional time series.
Prerequisites
Statistical inference and methods, Multivariate statistical analysis, Nonparametric smoothing methods