Introduction to functional data analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2017]
|
| Series: | Texts in statistical science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 290 Seiten Illustrationen, Diagramme |
| ISBN: | 9781032096599 9781498746342 |
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MARC
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Record in the Search Index
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| adam_text | Jontents
1 First steps in the analysis of functional data 1
1.1 Basis expansions.............................................. 3
1.2 Sample mean and covariance................................... 6
1.3 Principal component functions ............................... 10
1.4 Analysis of BOA stock returns................................ 11
1.5 Diffusion tensor imaging .................................... 14
1.6 Chapter 1 problems .......................................... 17
2 Further topics in exploratory FDA 21
2.1 Derivatives ................................................. 21
2.2 Penalized smoothing ....................................... 22
2.3 Curve alignment.............................................. 28
2.4 Further reading ............................................. 34
2.5 Chapter 2 problems ........................................ 34
։ 3 Mathematical framework for functional data 37
3.1 Square integrable functions ................................. 38
3.2 Random functions ............................................ 39
3.3 Linear transformations ...................................... 42
4 Scalar—on-function regression 45
4.1 Examples..................................................... 46
4.2 Review of standard regression theory ........................ 48
4.3 Difficulties specific to functional regression .............. 51
4.4 Estimation through a basis expansion ........................ 54
4.5 Estimation with a roughness penalty ......................... 56
4.6 Regression on functional principal components ............... 58
4.7 Implementation in the refund package......................... 60
4.8 Nonlinear scalar-on-function regression...................... 63
4.9 Chapter 4 problems ......................................... 64
5 Functional response models 67
5.1 Least squares estimation and application to angular motion . 67
5.2 Penalized least squares estimation .......................... 69
5.3 Functional regressors ....................................... 74
5.4 Penalized estimation in the refund package .................. 77
5.5 Estimation based on functional principal components .... 84
xi
xii Contents
5.6 Test of no effect .......................................... 87
5.7 Verification of the validity of a functional linear model ... 89
5.8 Extensions and further reading............................... 92
5.9 Chapter 5 Problems.......................................... 93
6 Functional generalized linear models 101
6.1 Background .............................................. 101
6.2 Scalar-on-function GLM’s.................................... 105
6.3 Functional response GLM..................................... 106
6.4 Implementation in the refund package........................ 107
6.5 Application to DTI ......................................... Ill
6.6 Further reading ............................................ 113
6.7 Chapter 6 problems ......................................... 114
7 Sparse FDA 117
7.1 Introduction ............................................... 117
7.2 Mean function estimation.................................. 122
7.3 Covariance function estimation.............................. 132
7.4 Sparse functional PCA ...................................... 134
7.5 Sparse functional regression . ............................. 137
7.6 Chapter 7 problems ......................................... 138
8 Functional time series 141
8.1 Fundamental concepts of time series analysis . ............. 141
8.2 Functional autoregressive process .......................... 145
8.3 Forecasting with the Hyndman-Ullah method .................. 148
8.4 Forecasting with multivariate predictors.................... 154
8.5 Long-run covariance function................................ 156
8.6 Testing stationarity of functional time series ............. 159
8.7 Generation and estimation of the FAR(l) model using package
fda . ...................................................... 165
8.8 Conditions for the existence of the FAR(l) process.......... 171
8.9 Further reading and other topics............................ 173
8.10 Chapter 8 problems ...................................... 174
9 Spatial functional data and models 179
9.1 Fundamental concepts of spatial statistics.................. 180
9.2 Functional spatial fields................................... 184
9.3 Functional kriging.......................................... 184
9.4 Mean function estimation.................................... 186
9.5 Implementation in the R package geof d ..................... 188
9.6 Other topics and further reading............................ 194
9.7 Chapter 9 problems ......................................... 206
Contents xiii
10 Elements of Hilbert space theory 211
10.1 Hilbert space............................................ 211
10.2 Projections and orthonormal sets .......................* 215
10.3 Linear operators......................................... 219
10.4 Basics of spectral theory ............................... 223
10.5 Tensors.................................................. 227
10.6 Chapter 10 problems ..................................... 230
11 Random functions 233
11.1 Random elements in metric spaces........................ 233
11.2 Expectation and covariance in a Hilbert space .......... 236
11.3 Gaussian functions and limit theorems .................. 239
11.4 Functional principal components.......................... 241
11.5 Chapter 11 problems ..................................... 245
12 Inference from a random sample 249
12.1 Consistency of sample mean and covariance functions .... 250
12.2 Estimated functional principal components ............... 253
12.3 Asymptotic normality..................................... 258
12.4 Hypothesis testing about the mean ....................... 261
12.5 Confidence bands for the mean .......................... 269
12.6 Application to BOA cumulative returns................... 272
12.7 Proof of Theorem 12.2.1 274
12.8 Chapter 12 problems ..................................... 276
References 279
Index
287
|
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| isbn | 9781032096599 9781498746342 |
| language | English |
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| spelling | Kokoszka, Piotr Verfasser (DE-588)171864093 aut Introduction to functional data analysis Piotr Kokoszka (Colorade State University, Ft. Collins, Colorado), Matthew Reimherr (The Pennsylvania State University, University Park, Pennsylvania) Boca Raton ; London ; New York CRC Press [2017] © 2017 xvi, 290 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Functional analysis Funktionale Datenanalyse (DE-588)4699227-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionale Datenanalyse (DE-588)4699227-3 s b DE-604 Reimherr, Matthew Verfasser (DE-588)1140075209 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029811026&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kokoszka, Piotr Reimherr, Matthew Introduction to functional data analysis Functional analysis Funktionale Datenanalyse (DE-588)4699227-3 gnd |
| subject_GND | (DE-588)4699227-3 (DE-588)4123623-3 |
| title | Introduction to functional data analysis |
| title_auth | Introduction to functional data analysis |
| title_exact_search | Introduction to functional data analysis |
| title_full | Introduction to functional data analysis Piotr Kokoszka (Colorade State University, Ft. Collins, Colorado), Matthew Reimherr (The Pennsylvania State University, University Park, Pennsylvania) |
| title_fullStr | Introduction to functional data analysis Piotr Kokoszka (Colorade State University, Ft. Collins, Colorado), Matthew Reimherr (The Pennsylvania State University, University Park, Pennsylvania) |
| title_full_unstemmed | Introduction to functional data analysis Piotr Kokoszka (Colorade State University, Ft. Collins, Colorado), Matthew Reimherr (The Pennsylvania State University, University Park, Pennsylvania) |
| title_short | Introduction to functional data analysis |
| title_sort | introduction to functional data analysis |
| topic | Functional analysis Funktionale Datenanalyse (DE-588)4699227-3 gnd |
| topic_facet | Functional analysis Funktionale Datenanalyse Lehrbuch |
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