Functional data analysis with R and MATLAB:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Series: | Use R!
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 207 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387981840 |
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MARC
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| 100 | 1 | |a Ramsay, James O. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Functional data analysis with R and MATLAB |c J. O. Ramsay ; Giles Hooker ; Spencer Graves |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XI, 207 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Datenverarbeitung | |
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Record in the Search Index
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| adam_text |
Contents
1
Introduction
to Functional Data Analysis
.,. 1
1.1
What Are Functional Data?
.,.
f
1.1.1
Data on the Growth of
Gîrb
. 1
1.1.2
Data on US Manufacturing
. 3
1.1.3
Input/Output Data for an OH Refinery
. 4
1.2
Muttïvariate
Functional Data
.,.». 5
1.2.1
Data on How Children Walk
.,. 5
1.2.2
Data on Handwriting
. 7
1.3
Functional Models for Nonfunctional Data
. 9
1.4
Some Functional Data Analyses
._.
!0
1.5
First Steps in a Functional Dam Analysis
_. 12
1.5.1
Data Representation: Smoothing and Interpolation
. 12
1.5.2
Data Registration or Feature Alignment
. 13
! .5.3
Graphing Functional Data
_. 14
1.5.4
Plotting Pairs of Derivatives; Phase-Plane Plots
. 15
1.6
Exploring Variability in Functional Data
.·. 16
1.6.1
Functional Descriptive Statistics
. 16
1.6.2
Functional Principal Components Analysis
. 16
.,6.3
Functional Canonical Correlation
.----- 17
1.7
Functional Linear Models
_. 17
1
.8
Using Derivatives in Functional Data Analysis
. 1 $
1
.9
Concluding Remarks
.,. 18
1.10
Some Things to Try
. 19
2
Essential Comparisons
öf
the
Matlab
and
R
Languages
_. 21
2.1
A Quick Comparison of
Matlab
and
R
Syntax
-----._. 21
2.1.1
Minor Differences
., —. 21
2.1.2
Using Functions in the Two Languages
. 2,1
2.2
Singleton Index Issues
. 24
2.3
Classes and Objects in
R
and
Matlab.
. 24
2.4
More to Read
.-----. —.-----. 26
Contents
How to Specify Basis Systems for Building Functions
. 29
3.Î
Basis Function Systems for Constructing Functions
. 29
3.2
Fourier Series for Periodic Data and Functions
. 32
3.3
Spline Series for Nonperiodic Data and Functions
. 33
3.3.1
Break Points and Knots
. 33
3.3.2
Order and Degree
. 34
3.3.3
Examples
. 34
3.3.4
B-Splines
. 35
3.3.5
Computational Issues Concerning the Range of
t
. 38
3.4
Constant, Monomial and Other Bases
. 39
3.4.1
The Constant Basis
. 39
3.4.2
The Monomial Basis
. 39
3.4.3
Other Basis Systems
. 40
3.5
Methods for Functional Basis Objects
. 40
3.6
The Structure of
tne basisf d
or basis Class
. 42
3.7
Some Things to Try
. 44
How to Build Functional Data Objects
. 45
4.Î
Adding Coefficients to Bases to Define Functions
._ 45
4.1.1
Coefficient Vectors, Matrices and Arrays
. 45
4.1.2
Labels for Functional Data Objects.
. 46
4.2
Methods for Functional Data Objects
. 48
4.2.1
Illustration: Sinusoidal Coefficients
. 50
4.3
Smoothing Using Regression Analysis
. 51
4.3.1
Plotting the January Thaw
. 52
4.4
The Linear Differential Operator or Lf
d
Class
. 55
4.5
Bivariate Functional Data Objects: Functions of Two Arguments
. 56
4.6
The Structure of the
f d
and Lf
d
Classes
. 57
4.7
Some Things to Try
_. 57
Smoothing:
Computing
Сигуеѕ
from Noisy Data
. 59
5.1
Regression Splines: Smoothing by Regression Analysis
. 59
5.2
Data Smoothing with Roughness Penalties
. 62
5.2.1
OroosHig a Roughness Penalty
. 62
5.2.2
The Roughness Penalty Matrix R.,.
. 64
5.2.3
The Smoothing or "Hat" Matrix and Degrees of Freedom
. 65
5.2.4
Defining Smoothing by Functional Parameter objects
. 66
5.2.5
Choosing Smoothing Parameter
Я
. 66
5.3
Case Study: The Log Precipitation Date
. 67
5.4
Positive, Monotone, Deesity and Other Constrained Functions
. 70
5.4Л
Positi¥ő
Smoothing
. 70
5.4.2
Moeotone Smoothing
._. 71
5.4.3
Probability Density Functions
. 74
5.5
AssessiBg
Ље
Fit to the Data
_. 77
5.6
Details for the
f
dPar Class and smooth
.
basis Function
. 78
Contents ix
5.6.1
The f
dPar
class
. 78
5.6.2
The smooth .basis Function
. 80
5.7
Some Things to Try
. 81
5.8
MoretoRead
. 82
6
Descriptions of Functional Date
.,_. 83
6.1
Some Functional Descriptive Statistics
. 83
6.1
Л
The BivariateCovarianceFunction v(s,t)
. 84
6.2
The Residual Variance-Covariance Matrix Ee
. 87
6.3
Functional Probes
Ρξ
. 87
6.4
Phase-Plane Plots of Periodic Effects
. 88
6.4.1
Phase-Plane Plots Show Energy Transfer
. 88
6.4.2
The Nondurable Goods Cycles
. 90
в
A3
Phase-Plane Plotting the Growth of Girls
. 91
6.5
Confidence Intervals for Curves and Their Derivatives
. 92
6.5.1
Two Linear Mappings Defining a Probe Value
._ 93
6.5.2
Computing Confidence Limits for Probe Values
. 95
6.5.3
Confidence Limits for Prince
Ruperťs
Log Precipitation
,. 95
6.6
Some Things to Try
. 96
7
Exploring Variation: Functional
Principal
and Canonical
Components Analysis
_. 99
7.1
An Overview of Functional PCA
._. 100
7.2
PCA with Function pea
.
f d
.102
7.2.1
PCA of the Log Precipitation Data
.103
7.2.2
PCA of Log Precipitation Residuals
.
Î
Ш
7.3
More Functional PCA Features
.,_,. 106
7.4
PCA of Joint X-Y Variation in Handwriting
. 108
7.5
Exploring Functional Covariation with Canonical Correlation
Analysis
.110
7.6
Details for the pea
.
f d
and
cca
.
f d
Functions
. 113
7.6.1
The pea
.
f d
Function
.113
7.6.2
The
cca
.
f
d
Function
.
,
.
î
14
7.7
Some Things to Try
._, 114
7.8
More to Read
. 115
8
Registration: Aligning
reatares
for Samples of Curves
_. 117
8.Î
Atnplttude and Phase Variation
. 117
8.2
Time-Warping Functions and Registration
. 119
8.3
Landmark Registratioa with Function ianctatarkreg
.121
8.4
Continuous Registration with
Functìon
register
.
f d
.
,
. 122
8.5
A Decomposition into Amplitude and Phase Sums of Squares
. 125
$.6
Registering the Chinese Handwriting Data
.126
8.7
Details for Functions landmarkreg and register
. £
й
. 127
8.7.1
Function landmarkreg
_. 12?
x
Contents
8.7.2
Function register
.
f d
.128
8.8
Some Things to Try
.129
8.9
More to Read
.130
9
Functional Linear Models for Scalar Responses
.13 !
9.1
Functional Linear Regression with a Scalar Response
.131
9.2
A Scalar Response Model for Log Annual Precipitation
.132
9.3
Setting Up the Functional Linear Model
.132
9.4
Three Estimates of the Regression Coefficient Predicting
Annual Precipitation
.133
9.4.Î
Low-Dimensional Regression Coefficient Function
β
. 134
9.4.2
Coefficient
β
Estimate Using a Roughness Penalty
.135
9.4.3
Choosing Smoothing Parameters
.138
9.4.4
Confidence Intervals
.,.140
9.4.5
Scalar Response Models by Functional Principal
Components
.141
9.5
Statistical Tests
.143
9.6
Some Things to Try
. 145
9.7
More to Read
.146
tO Linear Models for Functional Responses
.147
10.1
Functional Responses and an Analysis of Variance Model
.147
10.1.1
Climate Region Effects on Temperature
.147
10.1.2
Trends in Seabird Populations on Kodiak Island
. 149
10.
I
.3
Choosing Smoothing Parameters
.153
10.2
Functional Responses with Functional Predictors: The
Concurrent Model
.»._,.
Î54
10.2.1
Estimation for the Concurrent Model
_.155
Î
0.2.2
Confidence Intervals for Regression Functions
.157
10.2.3
Knee Angle Predicted from Hip Angle
.158
10.3
Beyond the Concurrent Model
.162
10.4
A Funcţionat
Linear Model for Swedish Mortality
. 163
10.5
Permutation Tests
oř
Functional Hypotheses
.165
10.5.1
Functional i-Tests
. 166
Ю.5.2
Functional F-Tcsts.
.168
10.6
Details for
R
Functions
f
Regress,
f
Regress
. €¥
anti
f
Regress
.
stđerr
.169
10.6.1
Function fRegress
._. 169
10.6.2
Function fRegress
. CV._173
10.6.3
Function fRegress
.
stderr
. 173
10.7
Details for Function piotbeta
.,.174
10.8
Details for Function linmod.
.,.174
10.9
Details for Functions Fperm
.
f d
and tperm.
f d
.175
10.9.
1 Function Fperm»
£
σ
,._
Î75
10.9.2
Function tperm. fd
.,.
17ft
Contents xi
10.10
Some
Things
to Try
.17?
10.11
More to Read
.,. 177
11
Functional Models and Dynamics
., 179
11.1
Introduction to Dynamics
.179
11.1.1
An Example of First-Order Dynamics
.180
11.1.2
Interpreting Second-Order Linear Dynamics
.181
11.1.3
Higher-Dimensional Linear Systems
.183
11.2
Principal Differential Analysis for Linear Dynamics
. 184
11.3
Principal Differential Analysis of the Lip Data
.185
1
1.4
PDA of the Handwriting Data
.187
11.5
Registration and PDA
. 190
11.6
Details for pda
.
f
d,
eigen.
pda, pda
.
overlay and
register
.
newf
d
.,.,.191
11.6.1
Function pda
.
f d
.191
11.6.2
Function
eigen.
pda
.192
11.6.3
Function pda
.
overlay
.,.193
11.6.4
Function register
.
newf
d
.193
11.7
Some Things to Try
.193
11.8
More to Read
.194
Symbol Table
. 197
References
._.199
Index
.203 |
| any_adam_object | 1 |
| author | Ramsay, James O. Hooker, Giles Graves, Spencer |
| author_facet | Ramsay, James O. Hooker, Giles Graves, Spencer |
| author_role | aut aut aut |
| author_sort | Ramsay, James O. |
| author_variant | j o r jo jor g h gh s g sg |
| building | Verbundindex |
| bvnumber | BV035406436 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278 |
| callnumber-search | QA278 |
| callnumber-sort | QA 3278 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CM 4400 QH 234 SK 850 ST 250 ST 601 |
| ctrlnum | (OCoLC)602526390 (DE-599)DNB992999650 |
| dewey-full | 519.5350285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5350285 |
| dewey-search | 519.5350285 |
| dewey-sort | 3519.5350285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Psychologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035406436 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T15:16:45Z |
| institution | BVB |
| isbn | 9780387981840 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017326992 |
| oclc_num | 602526390 |
| open_access_boolean | |
| owner | DE-945 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-11 DE-824 DE-634 DE-355 DE-BY-UBR |
| owner_facet | DE-945 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-11 DE-824 DE-634 DE-355 DE-BY-UBR |
| physical | XI, 207 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Use R! |
| spelling | Ramsay, James O. Verfasser aut Functional data analysis with R and MATLAB J. O. Ramsay ; Giles Hooker ; Spencer Graves New York, NY Springer 2009 XI, 207 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Use R! MATLAB Datenverarbeitung Multivariate analysis Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s R Programm (DE-588)4705956-4 s MATLAB (DE-588)4329066-8 s DE-604 Hooker, Giles Verfasser aut Graves, Spencer Verfasser aut Erscheint auch als Online-Ausgabe 978-0-387-98185-7 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017326992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramsay, James O. Hooker, Giles Graves, Spencer Functional data analysis with R and MATLAB MATLAB Datenverarbeitung Multivariate analysis Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd Datenanalyse (DE-588)4123037-1 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4123037-1 (DE-588)4329066-8 |
| title | Functional data analysis with R and MATLAB |
| title_auth | Functional data analysis with R and MATLAB |
| title_exact_search | Functional data analysis with R and MATLAB |
| title_full | Functional data analysis with R and MATLAB J. O. Ramsay ; Giles Hooker ; Spencer Graves |
| title_fullStr | Functional data analysis with R and MATLAB J. O. Ramsay ; Giles Hooker ; Spencer Graves |
| title_full_unstemmed | Functional data analysis with R and MATLAB J. O. Ramsay ; Giles Hooker ; Spencer Graves |
| title_short | Functional data analysis with R and MATLAB |
| title_sort | functional data analysis with r and matlab |
| topic | MATLAB Datenverarbeitung Multivariate analysis Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd Datenanalyse (DE-588)4123037-1 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB Datenverarbeitung Multivariate analysis Data processing R (Computer program language) R Programm Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017326992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ramsayjameso functionaldataanalysiswithrandmatlab AT hookergiles functionaldataanalysiswithrandmatlab AT gravesspencer functionaldataanalysiswithrandmatlab |