Plane answers to complex questions: the theory of linear models
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 455 - 462 |
| Beschreibung: | XIX, 473 S. graph. Darst. |
| ISBN: | 0387953612 |
Internformat
MARC
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| 084 | |a 15 |2 sdnb | ||
| 100 | 1 | |a Christensen, Ronald |d 1951- |e Verfasser |0 (DE-588)111351820 |4 aut | |
| 245 | 1 | 0 | |a Plane answers to complex questions |b the theory of linear models |c Ronald Christensen |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a XIX, 473 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer texts in statistics | |
| 500 | |a Literaturverz. S. 455 - 462 | ||
| 650 | 4 | |a Analyse de variance | |
| 650 | 7 | |a Modelos lineares (pesquisa;planejamento) |2 larpcal | |
| 650 | 4 | |a Modèles linéaires (Statistique) | |
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 4 | |a Analysis of variance | |
| 650 | 0 | 7 | |a Lineares Modell |0 (DE-588)4134827-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Lineares Modell |0 (DE-588)4134827-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009935514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009935514 | |
Datensatz im Suchindex
| _version_ | 1808045516930416640 |
|---|---|
| adam_text |
CONTENTS
PREFACE
TO
THE
THIRD
EDITION
VII
PREFACE
TO
THE
SECOND
EDITION
IX
PREFACE
TO
THE
FIRST
EDITION
XI
1
INTRODUCTION
1
1.1
RANDOM
VECTORS
AND
MATRICES
.
3
1.2
MULTIVARIATE
NORMAL
DISTRIBUTIONS
.
5
1.3
DISTRIBUTIONS
OF
QUADRATIC
FORMS
.
8
1.4
GENERALIZED
LINEAR
MODELS
.
13
1.5
ADDITIONAL
EXERCISES
.
15
2
ESTIMATION
18
2.1
IDENTIFIABILITY
AND
ESTIMABILITY
.
19
2.2
ESTIMATION:
LEAST
SQUARES
.
24
2.3
ESTIMATION:
BEST
LINEAR
UNBIASED
.
28
2.4
ESTIMATION:
MAXIMUM
LIKELIHOOD
.
30
2.5
ESTIMATION:
MINIMUM
VARIANCE
UNBIASED
.
30
2.6
SAMPLING
DISTRIBUTIONS
OF
ESTIMATES
.
32
2.7
GENERALIZED
LEAST
SQUARES
.
33
2.8
NORMAL
EQUATIONS
.
38
2.9
BAYESIAN
ESTIMATION
.
39
2.9.1
DISTRIBUTION
THEORY
.
43
XVI
CONTENTS
2.10
ADDITIONAL
EXERCISES
.
48
3
TESTING
HYPOTHESES
50
3.1
MORE
ABOUT
MODELS
.
51
3.2
TESTING
MODELS
.
53
3.2.1
A
GENERALIZED
TEST
PROCEDURE
.
60
3.3
TESTING
LINEAR
PARAMETRIC
FUNCTIONS
.
62
3.3.1
A
GENERALIZED
TEST
PROCEDURE
.
71
3.3.2
TESTING
AN
UNUSUAL
CLASS
OF
HYPOTHESES
.
74
3.4
TESTING
SINGLE
DEGREES
OF
FREEDOM
IN
A
GIVEN
SUBSPACE
.
.
76
3.5
DISCUSSION
.
77
3.6
BREAKING
A
SUM
OF
SQUARES
INTO
INDEPENDENT
COMPONENTS
.
78
3.6.1
TWO-WAY
ANOVA
.
79
3.6.2
GENERAL
THEORY
.
81
3.7
CONFIDENCE
REGIONS
.
85
3.8
TESTS
FOR
GENERALIZED
LEAST
SQUARES
MODELS
.
86
3.9
ADDITIONAL
EXERCISES
.
89
4
ONE-WAY
ANOVA
91
4.1
ANALYSIS
OF
VARIANCE
.
92
4.2
ESTIMATING
AND
TESTING
CONTRASTS
.
100
4.3
ADDITIONAL
EXERCISES
.
104
5
MULTIPLE
COMPARISON
TECHNIQUES
106
5.1
SCHEFFE
'
S
METHOD
.
107
5.2
LEAST
SIGNIFICANT
DIFFERENCE
METHOD
.
112
5.3
BONFERRONI
METHOD
.
113
5.4
TUKEY
'
S
METHOD
.
114
5.5
MULTIPLE
RANGE
TESTS:
NEWMAN-KEULS
AND
DUNCAN
.
115
5.6
SUMMARY
.
117
5.7
ADDITIONAL
EXERCISES
.
119
6
REGRESSION
ANALYSIS
122
6.1
SIMPLE
LINEAR
REGRESSION
.
123
6.2
MULTIPLE
REGRESSION
.
124
6.2.1
NONPARAMETRIC
REGRESSION
AND
GENERALIZED
ADDITIVE
MODELS
.
129
6.3
BEST
LINEAR
PREDICTION:
ANOTHER
APPROACH
TO
REGRESSION
.
.
130
6.4
MULTIPLE
CORRELATION
AND
THE
COEFFICIENT
OF
DETERMINATION
.
135
6.5
PARTIAL
CORRELATION
COEFFICIENTS
.
137
6.6
TESTING
LACK
OF
FIT
.
140
6.6.1
THE
TRADITIONAL
TEST
.
140
6.6.2
NEAR
REPLICATE
LACK
OF
FIT
TESTS
.
142
6.6.3
PARTITIONING
METHODS
.
145
6.7
POLYNOMIAL
REGRESSION
AND
ONE-WAY
ANALYSIS
OF
VARIANCE
.
148
CONTENTS
XVII
6.8
ADDITIONAL
EXERCISES
.
152
7
MULTIFACTOR
ANALYSIS
OF
VARIANCE
156
7.1
BALANCED
TWO-WAY
ANOVA
WITHOUT
INTERACTION
.
156
7.1.1
CONTRASTS
.
162
7.2
BALANCED
TWO-WAY
ANOVA
WITH
INTERACTION
.
163
7.2.1
INTERACTION
CONTRASTS
.
166
7.3
POLYNOMIAL
REGRESSION
AND
THE
BALANCED
TWO-WAY
ANOVA
172
7.4
TWO-WAY
ANOVA
WITH
PROPORTIONAL
NUMBERS
.
176
7.5
TWO-WAY
ANOVA
WITH
UNEQUAL
NUMBERS:
GENERAL
CASE
.
177
7.6
THREE
OR
MORE
WAY
ANALYSES
.
186
7.7
ADDITIONAL
EXERCISES
.
193
8
EXPERIMENTAL
DESIGN
MODELS
196
8.1
COMPLETELY
RANDOMIZED
DESIGNS
.
197
8.2
RANDOMIZED
COMPLETE
BLOCK
DESIGNS:
USUAL
THEORY
.
197
8.3
LATIN
SQUARE
DESIGNS
.
198
8.4
FACTORIAL
TREATMENT
STRUCTURES
.
202
8.5
MORE
ON
FACTORIAL
TREATMENT
STRUCTURES
.
205
8.6
ADDITIONAL
EXERCISES
.
207
9
ANALYSIS
OF
COVARIANCE
209
9.1
ESTIMATION
OF
FIXED
EFFECTS
.
211
9.2
ESTIMATION
OF
ERROR
AND
TESTS
OF
HYPOTHESES
.
213
9.3
APPLICATION:
MISSING
DATA
.
216
9.4
APPLICATION:
BALANCED
INCOMPLETE
BLOCK
DESIGNS
.
219
9.5
ADDITIONAL
EXERCISES
.
228
10
ESTIMATION
AND
TESTING
IN
GENERAL
GAUSS
-
MARKOV
MODELS
230
10.1
BLUES
WITH
AN
ARBITRARY
COVARIANCE
MATRIX
.
231
10.2
GEOMETRIC
ASPECTS
OF
ESTIMATION
.
237
10.3
HYPOTHESIS
TESTING
.
241
10.4
LEAST
SQUARES
CONSISTENT
ESTIMATION
.
246
11
SPLIT
PLOT
MODELS
254
11.1
A
CLUSTER
SAMPLING
MODEL
.
255
11.2
GENERALIZED
SPLIT
PLOT
MODELS
.
260
11.3
THE
SPLIT
PLOT
DESIGN
.
268
11.4
IDENTIFYING
THE
APPROPRIATE
ERROR
.
271
11.5
EXERCISE:
AN
UNUSUAL
SPLIT
PLOT
ANALYSIS
.
276
12
MIXED
MODELS
AND
VARIANCE
COMPONENTS
279
12.1
MIXED
MODELS
.
280
12.2
BEST
LINEAR
UNBIASED
PREDICTION
.
281
12.3
MIXED
MODEL
EQUATIONS
.
285
12.4
VARIANCE
COMPONENT
ESTIMATION:
MAXIMINN
LIKELIHOOD
.
.
287
XVIII
CONTENTS
12.5
MAXIMUM
LIKELIHOOD
ESTIMATION
FOR
SINGULAR
NORMAL
DIS
TRIBUTIONS
.
291
12.6
VARIANCE
COMPONENT
ESTIMATION:
REML
.
293
12.7
VARIANCE
COMPONENT
ESTIMATION:
MINQUE
.
295
12.8
VARIANCE
COMPONENT
ESTIMATION:
MIVQUE
.
298
12.9
VARIANCE
COMPONENT
ESTIMATION:
HENDERSON
'
S
METHOD
3
.
.
298
12.10
EXACT
F
TESTS
FOR
VARIANCE
COMPONENTS
.
302
12.10.1
WALD
'
S
TEST
.
302
12.10.2
OFVERSTEN
'
S
SECOND
METHOD
.
304
12.10.3
COMPARISON
OF
TESTS
.
306
12.11
RECOVERY
OF
INTERBLOCK
INFORMATION
IN
BIB
DESIGNS
.
309
12.11.1
ESTIMATION
.
310
12.11.2
MODEL
TESTING
.
313
12.11.3
CONTRASTS
.
316
12.11.4
ALTERNATIVE
INFERENTIAL
PROCEDURES
.
317
12.11.5
ESTIMATION
OF
VARIANCE
COMPONENTS
.
318
13
CHECKING
ASSUMPTIONS,
RESIDUALS,
AND
INFLUENTIAL
OBSER
VATIONS
320
13.1
LEVERAGE
.
323
13.1.1
MAHALANOBIS
DISTANCES
.
324
13.1.2
DIAGONAL
ELEMENTS
OF
THE
PROJECTION
OPERATOR
.
.
.
326
13.1.3
EXAMPLES
.
327
13.2
CHECKING
NORMALITY
.
333
13.2.1
OTHER
APPLICATIONS
FOR
NORMAL
PLOTS
.
338
13.3
CHECKING
INDEPENDENCE
.
341
13.3.1
SERIAL
CORRELATION
.
342
13.4
HETEROSCEDASTICITY
AND
LACK
OF
FIT
.
348
13.4.1
HETEROSCEDASTICITY
.
348
13.4.2
LACK
OF
FIT
.
355
13.5
UPDATING
FORMULAE
AND
PREDICTED
RESIDUALS
.
359
13.6
OUTLIERS
AND
INFLUENTIAL
OBSERVATIONS
.
363
13.7
TRANSFORMATIONS
.
366
14
VARIABLE
SELECTION
AND
COLLINEARITY
369
14.1
ALL
POSSIBLE
REGRESSIONS
AND
BEST
SUBSET
REGRESSION
.
370
14.1.1
R
2
.
371
14.1.2
ADJUSTED/?
2
.
371
14.1.3
MALLOWS
'
S
C
P
.
372
14.2
STEPWISE
REGRESSION
.
373
14.2.1
FORWARD
SELECTION
.
374
14.2.2
TOLERANCE
.
375
14.2.3
BACKWARD
ELIMINATION
.
375
14.2.4
OTHER
METHODS
.
376
14.3
DISCUSSION
OF
VARIABLE
SELECTION
TECHNIQUES
.
376
CONTENTS
XIX
14.4
DEFINING
COLLINEARITY
.
378
14.5
REGRESSION
IN
CANONICAL
FORM
AND
ON
PRINCIPAL
COMPONENTS
383
14.5.1
PRINCIPAL
COMPONENT
REGRESSION
.
386
14.5.2
GENERALIZED
INVERSE
REGRESSION
.
386
14.6
CLASSICAL
RIDGE
REGRESSION
.
387
14.7
MORE
ON
MEAN
SQUARED
ERROR
.
389
APPENDIX
A:
VECTOR
SPACES
391
APPENDIX
B:
MATRIX
RESULTS
399
B.L
BASIC
IDEAS
.
399
B.2
EIGENVALUES
AND
RELATED
RESULTS
.
401
B.3
PROJECTIONS
.
406
B.4
MISCELLANEOUS
RESULTS
.
415
B.5
PROPERTIES
OF
KRONECKER
PRODUCTS
AND
VEC
OPERATORS
.
416
B.6
TENSORS
.
418
B.7
EXERCISES
.
420
APPENDIX
C:
SOME
UNIVARIATE
DISTRIBUTIONS
424
APPENDIX
D:
MULTIVARIATE
DISTRIBUTIONS
428
APPENDIX
E:
INFERENCE
FOR
ONE
PARAMETER
432
E.L
CONFIDENCE
INTERVALS
.
433
E.2
HYPOTHESIS
TESTING
.
434
APPENDIX
F:
SIGNIFICANTLY
INSIGNIFICANT
TESTS
437
F.L
LACK
OF
FIT
AND
SMALL
F
STATISTICS
.
438
F.2
THE
EFFECT
OF
CORRELATION
AND
HETEROSCEDASTICITY
ON
F
STATIS
TICS
.
441
APPENDIX
G:
RANDOMIZATION
THEORY
MODELS
447
G.L
SIMPLE
RANDOM
SAMPLING
.
448
G.2
COMPLETELY
RANDOMIZED
DESIGNS
.
449
G.3
RANDOMIZED
COMPLETE
BLOCK
DESIGNS
.
451
REFERENCES
455
AUTHOR
INDEX
463
SUBJECT
INDEX
466 |
| any_adam_object | 1 |
| author | Christensen, Ronald 1951- |
| author_GND | (DE-588)111351820 |
| author_facet | Christensen, Ronald 1951- |
| author_role | aut |
| author_sort | Christensen, Ronald 1951- |
| author_variant | r c rc |
| building | Verbundindex |
| bvnumber | BV014615445 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279.C48 2002 |
| callnumber-search | QA279.C48 2002 |
| callnumber-sort | QA 3279 C48 42002 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 840 SK 915 |
| classification_tum | MAT 628f |
| ctrlnum | (OCoLC)47838546 (DE-599)BVBBV014615445 |
| dewey-full | 519.5/35 519.5/3521 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 519.5/35 21 |
| dewey-search | 519.5/35 519.5/35 21 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV014615445 |
| illustrated | Illustrated |
| indexdate | 2024-08-22T00:29:30Z |
| institution | BVB |
| isbn | 0387953612 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009935514 |
| oclc_num | 47838546 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-91G DE-BY-TUM DE-521 DE-83 DE-11 |
| owner_facet | DE-824 DE-703 DE-91G DE-BY-TUM DE-521 DE-83 DE-11 |
| physical | XIX, 473 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Christensen, Ronald 1951- Verfasser (DE-588)111351820 aut Plane answers to complex questions the theory of linear models Ronald Christensen 3. ed. New York [u.a.] Springer 2002 XIX, 473 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Literaturverz. S. 455 - 462 Analyse de variance Modelos lineares (pesquisa;planejamento) larpcal Modèles linéaires (Statistique) Linear models (Statistics) Analysis of variance Lineares Modell (DE-588)4134827-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineares Modell (DE-588)4134827-8 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009935514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Christensen, Ronald 1951- Plane answers to complex questions the theory of linear models Analyse de variance Modelos lineares (pesquisa;planejamento) larpcal Modèles linéaires (Statistique) Linear models (Statistics) Analysis of variance Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4123623-3 |
| title | Plane answers to complex questions the theory of linear models |
| title_auth | Plane answers to complex questions the theory of linear models |
| title_exact_search | Plane answers to complex questions the theory of linear models |
| title_full | Plane answers to complex questions the theory of linear models Ronald Christensen |
| title_fullStr | Plane answers to complex questions the theory of linear models Ronald Christensen |
| title_full_unstemmed | Plane answers to complex questions the theory of linear models Ronald Christensen |
| title_short | Plane answers to complex questions |
| title_sort | plane answers to complex questions the theory of linear models |
| title_sub | the theory of linear models |
| topic | Analyse de variance Modelos lineares (pesquisa;planejamento) larpcal Modèles linéaires (Statistique) Linear models (Statistics) Analysis of variance Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Analyse de variance Modelos lineares (pesquisa;planejamento) Modèles linéaires (Statistique) Linear models (Statistics) Analysis of variance Lineares Modell Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009935514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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