Introduction
Functional Data
Motivating Functional Data
Why Is Functional Data Analysis Needed?
Overview of the Book
Implementation of Methodologies
Options for Reading This Book
Nonparametric Smoothers for a Single Curve
Introduction
Local Polynomial Kernel Smoothing
Regression Splines
Smoothing Splines
P-Splines
Reconstruction of Functional Data
Introduction
Reconstruction Methods
Accuracy of LPK Reconstructions
Accuracy of LPK Reconstruction in FLMs
Stochastic Processes
Introduction
Stochastic Processes
x2-Type Mixtures
F-Type Mixtures
One-Sample Problem for Functional Data
ANOVA for Functional Data
Introduction
Two-Sample Problem
One-Way ANOVA
Two-Way ANOVA
Linear Models with Functional Responses
Introduction
Linear Models with Time-Independent Covariates
Linear Models with Time-Dependent Covariates
Ill-Conditioned Functional Linear Models
Introduction
Generalized Inverse Method
Reparameterization Method
Side-Condition Method
Diagnostics of Functional Observations
Introduction
Residual Functions
Functional Outlier Detection
Influential Case Detection
Robust Estimation of Coefficient Functions
Outlier Detection for a Sample of Functions
Heteroscedastic ANOVA for Functional Data
Introduction
Two-Sample Behrens-Fisher Problems
Heteroscedastic One-Way ANOVA
Heteroscedastic Two-Way ANOVA
Test of Equality of Covariance Functions
Introduction
Two-Sample Case
Multi-Sample Case
Bibliography
Index
Technical Proofs, Concluding Remarks, Bibliographical Notes, and Exercises appear at the end of most chapters.
Biography
Jin-Ting Zhang is an associate professor in the Department of Statistics and Applied Probability at the National University of Singapore. He has published extensively and has served on the editorial boards of several international statistical journals. He is the coauthor of Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effect Modelling Approaches and the coeditor of Advances in Statistics: Proceedings of the Conference in Honor of Professor Zhidong Bai on His 65th Birthday.
"… a focused presentation of functional ANOVA and linear function-on-scalar regression problems using the ‘smooth first’ approach to estimation and inference. I would recommend this book to anyone interested in theoretical developments and hypothesis testing in this commonly encountered class of problems."
—Jeff Goldsmith, Journal of the American Statistical Association, March 2014
