Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000003807629 | QA278 R35 1997 | Open Access Book | Book | Searching... |
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Summary
Summary
Scientists today collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields. Much of the material is based on the authors' own work, some of which appears here
Reviews 1
Choice Review
Samples of curves, or functional data, result from repeated measurements on units, typically observations over time at possibly irregular intervals. Ramsay and Silverman present statistical technology for examining samples of functional data. Their emphasis is on exploratory analyses to reveal new and interesting aspects of the data. Chapters offer introductory materials; discuss smoothing by fitting smooth functions and by applying roughness penalties; and discuss problems of curve registration; i.e., the alignment of common characteristics of a sample of curves. Other chapters examine principal component analyses for functional data; discuss functional analogues of linear models, models with scalar responses, and models with functional responses; explore the functional analogue of canonical correlation; and develop functional methods that exploit derivatives. Techniques are illustrated throughout with data from real applications. A thorough introduction to a collection of tools and techniques in an area of growing importance. Graduate students through professionals. F. Giesbrecht; North Carolina State University
Table of Contents
| Introduction |
| Notation and Techniques |
| Representing Functional Data as Smooth Functions |
| The Roughness Penalty Approach |
| The Registration and Display of Functional Data |
| Principal Components Analysis for Functional Data |
| Regularized Principal Components Analysis |
| Principal Components Analysis of Mixed Data |
| Functional Linear Models |
| Functional Linear Models for Scalar Responses |
| Functional Linear Modesl for Functional Responses |
| Canonical Correlation and Discriminant Analysis |
| Differential Operators in Functional Data Analysis |
| Principal Differential Analysis |
| More General Roughness Penalties |
| Some Perspectives on FDA |
