Analysis of Variance for Functional Data

Analysis of Variance for Functional Data (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

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

Chapter 1: Introduction
Chapter 2: Nonparametric Smoothers for a Single Curve
Chapter 3: Reconstruction of Functional Data
Chapter 4: Stochastic Processes
Chapter 5: ANOVA for Functional Data
Chapter 6: Linear Models with Functional Responses
Chapter 7: Ill-Conditioned Functional Linear Models
Chapter 8: Diagnostics of Functional Observations
Chapter 9: Heteroscedastic ANOVA for Functional Data
Chapter 10: Test of Equality of Covariance Functions