Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional linear models with functional responses, ill-conditioned functional linear models, diagnostics of functional observations, heteroscedastic ANOVA for functional data, and testing equality of covariance functions. Although the methodologies presented are designed for curve data, they can be extended to surface data.
Useful for statistical researchers and practitioners analyzing functional data, this self-contained book gives both a theoretical and applied treatment of functional data analysis supported by easy-to-use MATLAB® code. The author provides a number of simple methods for functional hypothesis testing. He discusses pointwise, L2-norm-based, F-type, and bootstrap tests.
Assuming only basic knowledge of statistics, calculus, and matrix algebra, the book explains the key ideas at a relatively low technical level using real data examples. Each chapter also includes bibliographical notes and exercises. Real functional data sets from the text and MATLAB codes for analyzing the data examples are available for download from the author’s website.
Table of Contents
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
Local Polynomial Kernel Smoothing
Reconstruction of Functional Data
Accuracy of LPK Reconstructions
Accuracy of LPK Reconstruction in FLMs
One-Sample Problem for Functional Data
ANOVA for Functional Data
Linear Models with Functional Responses
Linear Models with Time-Independent Covariates
Linear Models with Time-Dependent Covariates
Ill-Conditioned Functional Linear Models
Generalized Inverse Method
Diagnostics of Functional Observations
Functional Outlier Detection
Influential Case Detection
Robust Estimation of Coefficient Functions
Outlier Detection for a Sample of Functions
Heteroscedastic ANOVA for Functional Data
Two-Sample Behrens-Fisher Problems
Heteroscedastic One-Way ANOVA
Heteroscedastic Two-Way ANOVA
Test of Equality of Covariance Functions
Technical Proofs, Concluding Remarks, Bibliographical Notes, and Exercises appear at the end of most chapters.
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