Smoothing spline ANOVA models:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2002
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 261 - 271 |
| Physical Description: | XIII, 289 S. graph. Darst. |
| ISBN: | 0387953531 |
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MARC
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| 084 | |a MAT 654f |2 stub | ||
| 084 | |a MAT 628f |2 stub | ||
| 100 | 1 | |a Gu, Chong |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Smoothing spline ANOVA models |c Chong Gu |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a XIII, 289 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Literaturverz. S. 261 - 271 | ||
| 650 | 4 | |a Analyse de variance | |
| 650 | 4 | |a Lissage (Statistique) | |
| 650 | 4 | |a Splines, Théorie des | |
| 650 | 4 | |a Analysis of variance | |
| 650 | 4 | |a Smoothing (Statistics) | |
| 650 | 4 | |a Spline theory | |
| 650 | 0 | 7 | |a Glättung |0 (DE-588)4157404-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spline |0 (DE-588)4182391-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Varianzanalyse |0 (DE-588)4187413-4 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009715891 | |
Record in the Search Index
| _version_ | 1816444733170384896 |
|---|---|
| adam_text |
CONTENTS
PREFACE
VII
1
INTRODUCTION
1
1.1
ESTIMATION
PROBLEM
AND
METHOD
.
2
1.1.1
CUBIC
SMOOTHING
SPLINE
.
2
1.1.2
PENALIZED
LIKELIHOOD
METHOD
.
4
1.2
NOTATION
.
5
1.3
DECOMPOSITION
OF
MULTIVARIATE
FUNCTIONS
.
.
6
1.3.1
ANOVA
AND
AVERAGING
OPERATOR
.
6
1.3.2
MULTIWAY
ANOVA
DECOMPOSITION
.
7
1.3.3
MULTIVARIATE
STATISTICAL
MODELS
.
10
1.4
CASE
STUDIES
.
12
1.4.1
WATER
ACIDITY
IN
LAKES
.
12
1.4.2
AIDS
INCUBATION
.
14
1.4.3
SURVIVAL
AFTER
HEART
TRANSPLANT
.
15
1.5
SCOPE
.
17
1.6
BIBLIOGRAPHIC
NOTES
.
18
1.7
PROBLEMS
.
19
2
MODEL
CONSTRUCTION
21
2.1
REPRODUCING
KERNEL
HILBERT
SPACES
.
22
2.1.1
HILBERT
SPACES
AND
LINEAR
SUBSPACES
.
22
2.1.2
RIESZ
REPRESENTATION
THEOREM
.
27
X
CONTENTS
2.1.3
REPRODUCING
KERNEL
AND
NON-NEGATIVE
DEFINITE
FUNCTION
.
27
2.2
SMOOTHING
SPLINES
ON
{1,.,
K}
.
30
2.3
POLYNOMIAL
SMOOTHING
SPLINES
ON
[0,1]
.
32
2.3.1
A
REPRODUCING
KERNEL
IN
1]
.
32
2.3.2
COMPUTATION
OF
POLYNOMIAL
SMOOTHING
SPLINES
.
34
2.3.3
ANOTHER
REPRODUCING
KERNEL
IN
[0,1]
.
35
2.4
SMOOTHING
SPLINES
ON
PRODUCT
DOMAINS
.
38
2.4.1
TENSOR
PRODUCT
REPRODUCING
KERNEL
HILBERT
SPACES
.
38
2.4.2
REPRODUCING
KERNEL
HILBERT
SPACES
ON
{1,.,K}
2
.
39
2.4.3
REPRODUCING
KERNEL
HILBERT
SPACES
ON
[0,
1]
2
.
.
.
.
40
2.4.4
REPRODUCING
KERNEL
HILBERT
SPACES
ON
{1,.,R}
X
[0,1]
.
43
2.4.5
MULTIPLE-TERM
REPRODUCING
KERNEL
HILBERT
SPACES
.
43
2.5
BAYES
MODEL
.
46
2.5.1
SHRINKAGE
ESTIMATES
AS
BAYES
ESTIMATES
.
46
2.5.2
POLYNOMIAL
SPLINES
AS
BAYES
ESTIMATES
.
47
2.5.3
SMOOTHING
SPLINES
AS
BAYES
ESTIMATES
.
49
2.6
MINIMIZATION
OF
PENALIZED
FUNCTIONAL
.
50
2.6.1
EXISTENCE
OF
MINIMIZER
.
50
2.6.2
PENALIZED
AND
CONSTRAINED
OPTIMIZATION
.
52
2.7
BIBLIOGRAPHIC
NOTES
.
53
2.8
PROBLEMS
.
55
3
REGRESSION
WITH
GAUSSIAN-TYPE
RESPONSES
59
3.1
PRELIMINARIES
.
60
3.2
SMOOTHING
PARAMETER
SELECTION
.
62
3.2.1
UNBIASED
ESTIMATE
OF
RELATIVE
LOSS
.
63
3.2.2
GENERALIZED
CROSS-VALIDATION
.
65
3.2.3
RESTRICTED
MAXIMUM
LIKELIHOOD
.
68
3.2.4
WEIGHTED
AND
REPLICATED
DATA
.
69
3.2.5
EMPIRICAL
PERFORMANCE
.
70
3.3
BAYESIAN
CONFIDENCE
INTERVALS
.
72
3.3.1
POSTERIOR
DISTRIBUTION
.
72
3.3.2
CONFIDENCE
INTERVALS
ON
SAMPLING
POINTS
.
74
3.3.3
ACROSS-THE-FUNCTION
COVERAGE
.
75
3.4
COMPUTATION:
GENERIC
ALGORITHMS
.
76
3.4.1
ALGORITHM
FOR
FIXED
SMOOTHING
PARAMETERS
.
76
3.4.2
ALGORITHM
FOR
SINGLE
SMOOTHING
PARAMETER
.
77
3.4.3
ALGORITHM
FOR
MULTIPLE
SMOOTHING
PARAMETERS
.
79
3.4.4
CALCULATION
OF
POSTERIOR
VARIANCES
.
80
3.5
SOFTWARE
.
81
CONTENTS
XI
3.5.1
REPACK
.
81
3.5.2
R
PACKAGE
GSS
.
82
3.6
MODEL
CHECKING
TOOLS
.
86
3.6.1
COSINE
DIAGNOSTICS
.
87
3.6.2
EXAMPLES
.
87
3.6.3
CONCEPTS
AND
HEURISTICS
.
91
3.7
CASE
STUDIES
.
93
3.7.1
NITROGEN
OXIDES
IN
ENGINE
EXHAUST
.
93
3.7.2
OZONE
CONCENTRATION
IN
LOS
ANGELES
BASIN
.
94
3.8
COMPUTATION:
SPECIAL
ALGORITHMS
.
99
3.8.1
FAST
ALGORITHM
FOR
POLYNOMIAL
SPLINES
.
100
3.8.2
MONTE
CARLO
CROSS-VALIDATION
.
101
3.9
BIBLIOGRAPHIC
NOTES
.
103
3.10
PROBLEMS
.
105
4
MORE
SPLINES
111
4.1
PARTIAL
SPLINES
.
112
4.2
SPLINES
ON
THE
CIRCLE
.
113
4.2.1
PERIODIC
REPRODUCING
KERNEL
HILBERT
SPACES
.
114
4.2.2
SPLINES
AS
LOW-PASS
FILTERS
.
114
4.2.3
MORE
ON
ASYMPTOTICS
OF
§3.2
.
116
4.3
L-SPLINES
.
119
4.3.1
TRIGONOMETRIC
SPLINES
.
120
4.3.2
CHEBYSHEV
SPLINES
.
122
4.3.3
GENERAL
CONSTRUCTION
.
126
4.3.4
CASE
STUDY:
WEIGHT
LOSS
OF
OBESE
PATIENT
.
130
4.3.5
FAST
ALGORITHM
.
134
4.4
THIN-PLATE
SPLINES
.
135
4.4.1
SEMI-KERNELS
FOR
THIN-PLATE
SPLINES
.
136
4.4.2
REPRODUCING
KERNELS
FOR
THIN-PLATE
SPLINES
.
138
4.4.3
TENSOR
PRODUCT
THIN-PLATE
SPLINES
.
140
4.4.4
CASE
STUDY:
WATER
ACIDITY
IN
LAKES
.
141
4.5
BIBLIOGRAPHIC
NOTES
.
143
4.6
PROBLEMS
.
144
5
REGRESSION
WITH
EXPONENTIAL
FAMILIES
149
5.1
PRELIMINARIES
.
150
5.2
SMOOTHING
PARAMETER
SELECTION
.
151
5.2.1
PERFORMANCE-ORIENTED
ITERATION
.
152
5.2.2
DIRECT
CROSS-VALIDATION
.
155
5.2.3
EMPIRICAL
PERFORMANCE
.
158
5.3
APPROXIMATE
BAYESIAN
CONFIDENCE
INTERVALS
.
159
5.4
SOFTWARE:
R
PACKAGE
GSS
.
161
5.4.1
BINOMIAL
FAMILY
.
162
5.4.2
POISSON
FAMILY
.
163
XII
CONTENTS
5.4.3
GAMMA
FAMILY
.
164
5.4.4
INVERSE
GAUSSIAN
FAMILY
.
165
5.4.5
NEGATIVE
BINOMIAL
FAMILY
.
166
5.5
CASE
STUDIES
.
168
5.5.1
ERUPTION
TIME
OF
OLD
FAITHFUL
.
168
5.5.2
SPECTRUM
OF
YEARLY
SUNSPOTS
.
170
5.5.3
PROGRESSION
OF
DIABETIC
RETINOPATHY
.
171
5.6
BIBLIOGRAPHIC
NOTES
.
173
5.7
PROBLEMS
.
175
6
PROBABILITY
DENSITY
ESTIMATION
177
6.1
PRELIMINARIES
.
178
6.2
POISSON
INTENSITY
.
182
6.3
SMOOTHING
PARAMETER
SELECTION
.
183
6.3.1
KULLBACK-LEIBLER
LOSS
AND
CROSS-VALIDATION
.
183
6.3.2
MODIFICATIONS
OF
CROSS-VALIDATION
SCORE
.
185
6.3.3
EMPIRICAL
PERFORMANCE
.
187
6.4
COMPUTATION
.
187
6.5
CASE
STUDIES
.
190
6.5.1
BUFFALO
SNOWFALL
.
190
6.5.2
ERUPTION
TIME
OF
OLD
FAITHFUL
.
191
6.5.3
AIDS
INCUBATION
.
191
6.6
BIASED
SAMPLING
AND
RANDOM
TRUNCATION
.
192
6.6.1
BIASED
AND
TRUNCATED
SAMPLES
.
193
6.6.2
PENALIZED
LIKELIHOOD
ESTIMATION
.
194
6.6.3
EMPIRICAL
PERFORMANCE
.
196
6.6.4
CASE
STUDY:
AIDS
INCUBATION
.
198
6.7
CONDITIONAL
DENSITIES
.
198
6.7.1
PENALIZED
LIKELIHOOD
ESTIMATION
.
199
6.7.2
CASE
STUDY:
PENNY
THICKNESS
.
200
6.7.3
LOGISTIC
REGRESSION
.
202
6.8
RESPONSE-BASED
SAMPLING
.
204
6.8.1
RESPONSE-BASED
SAMPLES
.
204
6.8.2
PENALIZED
LIKELIHOOD
ESTIMATION
.
206
6.9
BIBLIOGRAPHIC
NOTES
.
206
6.10
PROBLEMS
.
209
7
HAZARD
RATE
ESTIMATION
211
7.1
PRELIMINARIES
.
212
7.2
SMOOTHING
PARAMETER
SELECTION
.
214
7.2.1
KULLBACK-LEIBLER
LOSS
AND
CROSS-VALIDATION
.
215
7.2.2
EMPIRICAL
PERFORMANCE
.
217
7.3
CASE
STUDIES
.
218
7.3.1
TREATMENTS
OF
GASTRIC
CANCER
.
218
7.3.2
SURVIVAL
AFTER
HEART
TRANSPLANT
.
219
CONTENTS
XIII
7.4
PENALIZED
PARTIAL
LIKELIHOOD
.
221
7.4.1
PARTIAL
LIKELIHOOD
AND
BIASED
SAMPLING
.
221
7.4.2
CASE
STUDY:
SURVIVAL
AFTER
HEART
TRANSPLANT
.
221
7.5
MODELS
PARAMETRIC
IN
TIME
.
222
7.5.1
ACCELERATED
LIFE
MODELS
.
222
7.5.2
WEIBULL
FAMILY
.
224
7.5.3
LOG
NORMAL
FAMILY
.
225
7.5.4
LOG
LOGISTIC
FAMILY
.
226
7.5.5
CASE
STUDY:
SURVIVAL
AFTER
HEART
TRANSPLANT
.
227
7.6
BIBLIOGRAPHIC
NOTES
.
228
7.7
PROBLEMS
.
230
8
ASYMPTOTIC
CONVERGENCE
231
8.1
PRELIMINARIES
.
231
8.2
RATES
FOR
DENSITY
ESTIMATES
.
234
8.2.1
LINEAR
APPROXIMATION
.
235
8.2.2
APPROXIMATION
ERROR
AND
MAIN
RESULTS
.
237
8.2.3
SEMIPARAMETRIC
APPROXIMATION
.
239
8.2.4
CONVERGENCE
UNDER
INCORRECT
MODEL
.
242
8.2.5
ESTIMATION
UNDER
BIASED
SAMPLING
.
243
8.2.6
ESTIMATION
OF
CONDITIONAL
DENSITY
.
244
8.2.7
ESTIMATION
UNDER
RESPONSE-BASED
SAMPLING
.
245
8.3
RATES
FOR
HAZARD
ESTIMATES
.
245
8.3.1
MARTINGALE
STRUCTURE
.
246
8.3.2
LINEAR
APPROXIMATION
.
247
8.3.3
APPROXIMATION
ERROR
AND
MAIN
RESULT
.
248
8.3.4
SEMIPARAMETRIC
APPROXIMATION
.
250
8.3.5
CONVERGENCE
UNDER
INCORRECT
MODEL
.
253
8.4
RATES
FOR
REGRESSION
ESTIMATES
.
253
8.4.1
GENERAL
FORMULATION
.
254
8.4.2
LINEAR
APPROXIMATION
.
254
8.4.3
APPROXIMATION
ERROR
AND
MAIN
RESULT
.
255
8.4.4
CONVERGENCE
UNDER
INCORRECT
MODEL
.
257
8.5
BIBLIOGRAPHIC
NOTES
.
258
8.6
PROBLEMS
.
259
REFERENCES
261
AUTHOR
INDEX
273
SUBJECT
INDEX
277 |
| any_adam_object | 1 |
| author | Gu, Chong |
| author_facet | Gu, Chong |
| author_role | aut |
| author_sort | Gu, Chong |
| author_variant | c g cg |
| building | Verbundindex |
| bvnumber | BV014173135 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279 |
| callnumber-search | QA279 |
| callnumber-sort | QA 3279 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 QH 236 SK 830 SK 840 |
| classification_tum | MAT 654f MAT 628f |
| ctrlnum | (OCoLC)47831606 (DE-599)BVBBV014173135 |
| dewey-full | 519.5/38 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/38 |
| dewey-search | 519.5/38 |
| dewey-sort | 3519.5 238 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV014173135 |
| illustrated | Illustrated |
| indexdate | 2024-11-22T17:31:26Z |
| institution | BVB |
| isbn | 0387953531 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009715891 |
| oclc_num | 47831606 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 |
| physical | XIII, 289 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Gu, Chong Verfasser aut Smoothing spline ANOVA models Chong Gu New York [u.a.] Springer 2002 XIII, 289 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 261 - 271 Analyse de variance Lissage (Statistique) Splines, Théorie des Analysis of variance Smoothing (Statistics) Spline theory Glättung (DE-588)4157404-7 gnd rswk-swf Spline (DE-588)4182391-6 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 s Spline (DE-588)4182391-6 s Glättung (DE-588)4157404-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715891&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gu, Chong Smoothing spline ANOVA models Analyse de variance Lissage (Statistique) Splines, Théorie des Analysis of variance Smoothing (Statistics) Spline theory Glättung (DE-588)4157404-7 gnd Spline (DE-588)4182391-6 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| subject_GND | (DE-588)4157404-7 (DE-588)4182391-6 (DE-588)4187413-4 |
| title | Smoothing spline ANOVA models |
| title_auth | Smoothing spline ANOVA models |
| title_exact_search | Smoothing spline ANOVA models |
| title_full | Smoothing spline ANOVA models Chong Gu |
| title_fullStr | Smoothing spline ANOVA models Chong Gu |
| title_full_unstemmed | Smoothing spline ANOVA models Chong Gu |
| title_short | Smoothing spline ANOVA models |
| title_sort | smoothing spline anova models |
| topic | Analyse de variance Lissage (Statistique) Splines, Théorie des Analysis of variance Smoothing (Statistics) Spline theory Glättung (DE-588)4157404-7 gnd Spline (DE-588)4182391-6 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| topic_facet | Analyse de variance Lissage (Statistique) Splines, Théorie des Analysis of variance Smoothing (Statistics) Spline theory Glättung Spline Varianzanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715891&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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