Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Helps any serious data analyst with a computer to recognize the strengths and limitations of data, to test the assumptions implicit in the least squares methods used to fit the data, to select appropriate forms of the variables, to judge which combinations of variables are most influential, and to state the conditions under which the fitted equations are applicable. This edition includes numerous extensions and new devices such as component and component-plus-residual plots, cross verification with a second sample, and an index of required x-precision; also, the search for better subset equations is enlarged to cover 262,144 alternatives. The methods described have been applied in agricultural, environmental, management, marketing, medical, physical, and social sciences. Mathematics is kept to the level of college algebra.