Functional Data AnalysisSpringer Science & Business Media, 2013 M11 11 - 311 páginas 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 for the first time. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He draws on his collaboration with researchers in speech articulation, motor control, meteorology, psychology, and human physiology to illustrate his technical contributions to functional data analysis in a wide range of statistical and application journals. Bernard Silverman, author of the highly regarded "Density Estimation for Statistics and Data Analysis," and coauthor of "Nonparametric Regression and Generalized Linear Models: A Roughness Penalty |
Contenido
| 1 | |
| 2 | |
| 4 | |
Regularized principal components analysis | 7 |
Principal differential analysis | 14 |
Principal differential analysis | 20 |
Some extended uses of inner product notation | 30 |
16 | 53 |
Functional linear models for scalar responses | 157 |
Functional linear models for functional responses | 178 |
Canonical correlation and discriminant analysis | 199 |
Differential operators in functional data analysis | 217 |
More general roughness penalties | 257 |
Some perspectives on FDA | 277 |
Some algebraic and functional techniques 285 | 284 |
| 293 | |
The registration and display of functional data | 67 |
Principal components analysis for functional data | 84 |
Introduction | 125 |
Functional linear models | 141 |
| 303 | |
| 306 | |
Otras ediciones - Ver todas
Términos y frases comunes
acceleration algorithm applied approach approximation argument values B-splines basis expansion basis functions canonical correlation canonical correlation analysis canonical variates Chapter coefficients computation consider constraint context corresponding covariance criterion cross-validation curves defined diagonal differential equation discrete discussed displays effect eigenanalysis eigenvalue eigenvector error estimated example Figure Fourier series function ẞ functional data analysis functional linear model functional observations gait data Hip angle inner product inner product spaces integral interpolation kernel knee angles least squares linear combination linear differential operator linear model log precipitation matrix maximizing mean measure minimizing multivariate notation orthogonal overall penalized plot polynomial prediction principal components analysis problem properties regression REGSSE regularization residual sum roughness penalty sample satisfies scores second derivative Section shift Silverman smoothing parameter solution space spline spline smoothing statistics sum of squares techniques transformation variability variance vector weather stations weight functions zero