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Functional Data Analysis with R and MATLAB
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Functional Data Analysis with R and MATLAB
von: James O. Ramsay, Giles Hooker, Spencer Graves
Springer-Verlag, 2009
ISBN: 9780387981857
202 Seiten, Download: 4315 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Preface 5  
  Contents 7  
  Introduction to Functional Data Analysis 12  
     1.1 What Are Functional Data? 12  
     1.2 Multivariate Functional Data 16  
     1.3 Functional Models for Nonfunctional Data 20  
     1.4 Some Functional Data Analyses 21  
     1.5 First Steps in a Functional Data Analysis 23  
     1.6 Exploring Variability in Functional Data 27  
     1.7 Functional Linear Models 28  
     1.8 Using Derivatives in Functional Data Analysis 29  
     1.9 Concluding Remarks 29  
     1.10 Some Things to Try 30  
  Essential Comparisons of the Matlab and R Languages 31  
     2.1 A Quick Comparison of Matlab and R Syntax 31  
     2.2 Singleton Index Issues 34  
     2.3 Classes and Objects in R and Matlab 34  
     2.4 More to Read 36  
  How to Specify Basis Systems for Building Functions 38  
     3.1 Basis Function Systems for Constructing Functions 38  
     3.2 Fourier Series for Periodic Data and Functions 41  
     3.3 Spline Series for Nonperiodic Data and Functions 42  
     3.4 Constant, Monomial and Other Bases 48  
     3.5 Methods for Functional Basis Objects 49  
     3.6 The Structure of the basisfd or basis Class 51  
     3.7 Some Things to Try 53  
  How to Build Functional Data Objects 54  
     4.1 Adding Coefficients to Bases to Define Functions 54  
     4.2 Methods for Functional Data Objects 57  
     4.3 Smoothing Using Regression Analysis 60  
     4.4 The Linear Differential Operator or Lfd Class 64  
     4.5 Bivariate Functional Data Objects: Functions of Two Arguments 65  
     4.6 The Structure of the fd and Lfd Classes 66  
     4.7 Some Things to Try 66  
  Smoothing: Computing Curves from Noisy Data 68  
     5.1 Regression Splines: Smoothing by Regression Analysis 68  
     5.2 Data Smoothing with Roughness Penalties 71  
     5.3 Case Study: The Log Precipitation Data 76  
     5.4 Positive, Monotone, Density and Other Constrained Functions 79  
     5.5 Assessing the Fit to the Data 86  
     5.6 Details for the fdPar Class and smooth. basis Function 87  
     5.7 Some Things to Try 90  
     5.8 More to Read 91  
  Descriptions of Functional Data 92  
     6.1 Some Functional Descriptive Statistics 92  
     6.2 The Residual Variance-Covariance Matrix Se 96  
     6.3 Functional Probes rx 96  
     6.4 Phase-Plane Plots of Periodic Effects 97  
     6.5 Confidence Intervals for Curves and Their Derivatives 101  
     6.6 Some Things to Try 105  
  Exploring Variation: Functional Principal and Canonical Components Analysis 107  
     7.1 An Overview of Functional PCA 108  
     7.2 PCA with Function pca. fd 110  
     7.3 More Functional PCA Features 114  
     7.4 PCA of Joint X-Y Variation in Handwriting 116  
     7.5 Exploring Functional Covariation with Canonical Correlation Analysis 118  
     7.6 Details for the pca. fd and cca. fd Functions 121  
     7.7 Some Things to Try 122  
     7.8 More to Read 123  
  Registration: Aligning Features for Samples of Curves 124  
     8.1 Amplitude and Phase Variation 124  
     8.2 Time-Warping Functions and Registration 126  
     8.3 Landmark Registration with Function landmarkreg 128  
     8.4 Continuous Registration with Function register. fd 129  
     8.5 A Decomposition into Amplitude and Phase Sums of Squares 132  
     8.6 Registering the Chinese Handwriting Data 133  
     8.7 Details for Functions landmarkreg and register. fd 134  
     8.8 Some Things to Try 136  
     8.9 More to Read 137  
  Functional Linear Models for Scalar Responses 138  
     9.1 Functional Linear Regression with a Scalar Response 138  
     9.2 A Scalar Response Model for Log Annual Precipitation 139  
     9.3 Setting Up the Functional Linear Model 139  
     9.4 Three Estimates of the Regression Coefficient Predicting Annual Precipitation 140  
     9.5 Statistical Tests 150  
     9.6 Some Things to Try 152  
     9.7 More to Read 153  
  Linear Models for Functional Responses 154  
     10.1 Functional Responses and an Analysis of Variance Model 154  
     10.2 Functional Responses with Functional Predictors: The Concurrent Model 161  
     10.3 Beyond the Concurrent Model 169  
     10.4 A Functional Linear Model for Swedish Mortality 170  
     10.5 Permutation Tests of Functional Hypotheses 172  
     10.6 Details for R Functions fRegress, fRegress. CV and fRegress. stderr 176  
     10.7 Details for Function plotbeta 181  
     10.8 Details for Function linmod 181  
     10.9 Details for Functions Fperm. fd and tperm. fd 182  
     10.10 Some Things to Try 184  
     10.11 More to Read 184  
  Functional Models and Dynamics 185  
     11.1 Introduction to Dynamics 185  
     11.2 Principal Differential Analysis for Linear Dynamics 190  
     11.3 Principal Differential Analysis of the Lip Data 191  
     11.4 PDA of the Handwriting Data 193  
     11.5 Registration and PDA 196  
     11.6 Details for pda.fd, eigen.pda, pda. overlay and register. newfd 197  
     11.7 Some Things to Try 199  
     11.8 More to Read 200  
  Symbol Table 202  
  References 204  
  Index 208  


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