Analysis of Variance for Functional Data

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.

Introduction Functional Data Motivating Functional DataWhy 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 SmoothingRegression SplinesSmoothing SplinesP-Splines Reconstruction of Functional Data Introduction Reconstruction MethodsAccuracy of LPK ReconstructionsAccuracy of LPK Reconstruction in FLMs Stochastic Processes Introduction Stochastic Processesx2-Type Mixtures F-Type Mixtures One-Sample Problem for Functional Data ANOVA for Functional Data Introduction Two-Sample ProblemOne-Way ANOVATwo-Way ANOVA Linear Models with Functional Responses Introduction Linear Models with Time-Independent CovariatesLinear Models with Time-Dependent Covariates Ill-Conditioned Functional Linear Models Introduction Generalized Inverse MethodReparameterization MethodSide-Condition Method Diagnostics of Functional Observations Introduction Residual FunctionsFunctional Outlier DetectionInfluential Case Detection Robust Estimation of Coefficient Functions Outlier Detection for a Sample of Functions Heteroscedastic ANOVA for Functional Data Introduction Two-Sample Behrens-Fisher ProblemsHeteroscedastic One-Way ANOVAHeteroscedastic Two-Way ANOVA Test of Equality of Covariance Functions IntroductionTwo-Sample CaseMulti-Sample Case Bibliography Index 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.