Plane answers to complex questions: the theory of linear models
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1996
|
| Edition: | 2. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 433 - 439 |
| Physical Description: | XVII, 452 S. graph. Darst. |
| ISBN: | 0387947671 |
Staff View
MARC
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| 245 | 1 | 0 | |a Plane answers to complex questions |b the theory of linear models |c Ronald Christensen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XVII, 452 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer texts in statistics | |
| 500 | |a Literaturverz. S. 433 - 439 | ||
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
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 Additional Exercises 12
2 Estimation 16
2.1 Estimability 17
2.2 Estimation: Least Squares 20
2.3 Estimation: Best Linear Unbiased 23
2.4 Estimation: Maximum Likelihood 25
2.5 Estimation: Minimum Variance Unbiased 25
2.6 Sampling Distributions of Estimates 27
2.7 Weighted Least Squares 28
2.8 Normal Equations 33
2.9 Bayesian Estimation 33
2.9.1 Distribution Theory 38
2.10 Additional Exercises 42
xiv Contents
3 Testing Hypotheses 45
3.1 More About Models 46
3.2 Testing Models 47
3.2.1 Breaking Up Sums of Squares 54
3.2.2 A Generalized Test Procedure 56
3.3 Testing Linear Parametric Functions 58
3.3.1 A Generalized Test Procedure 62
3.3.2 Testing an Unusual Class of Hypotheses 64
3.4 Testing Single Degrees of Freedom in a Given Subspace . 66
3.5 Discussion 67
3.6 Breaking a Sum of Squares into Independent Components 68
3.7 Confidence Regions 73
3.8 Tests for Weighted Least Squares Models 74
3.9 Additional Exercises 77
4 One Way ANOVA 79
4.1 Analysis of Variance 80
4.2 Estimating and Testing Contrasts 88
4.3 Additional Exercises 92
5 Multiple Comparison Techniques 94
5.1 Scheffe s Method 95
5.2 Least Significant Difference Method 100
5.3 Bonferroni Method 101
5.4 Tukey s Method 102
5.5 Multiple Range Tests: Newman Keuls and Duncan .... 103
5.6 Summary 105
5.7 Additional Exercises 107
6 Regression Analysis 110
6.1 Simple Linear Regression Ill
6.2 Multiple Regression 112
6.3 Best Linear Prediction: Another Approach to Regression . 117
6.4 Multiple Correlation and the Coefficient of Determination 122
6.5 Partial Correlation Coefficients 124
6.6 Testing Lack of Fit 127
6.6.1 The Traditional Test 127
6.6.2 Near Replicate Lack of Fit Tests 129
6.6.3 Partitioning Methods 132
6.7 Polynomial Regression and One Way Analysis of Variance 135
6.8 Additional Exercises 139
7 Multifactor Analysis of Variance 143
7.1 Balanced Two Way ANOVA Without Interaction 143
7.1.1 Contrasts 149
Contents xv
7.2 Balanced Two Way ANOVA with Interaction 150
7.2.1 Interaction Contrasts 153
7.3 Polynomial Regression and the Balanced Two Way ANOVA 159
7.4 Two Way ANOVA with Proportional Numbers 163
7.5 Two Way ANOVA with Unequal Numbers: General Case . 164
7.6 Three or More Way Analyses 173
7.7 Additional Exercises 180
8 Experimental Design Models 183
8.1 Completely Randomized Designs 184
8.2 Randomized Complete Block Designs: Usual Theory . . . 184
8.3 Latin Square Designs 185
8.4 Factorial Treatment Structures 189
8.5 Additional Exercises 192
9 Analysis of Covariance 193
9.1 Estimation of Fixed Effects 195
9.2 Estimation of Error and Tests of Hypotheses 196
9.3 Application: Missing Data 200
9.4 Application: Balanced Incomplete Block Designs 202
9.5 Additional Exercises 211
10 Estimation and Testing in General Gauss Markov Models 213
10.1 BLUEs with an Arbitrary Covariance Matrix 214
10.2 Geometric Aspects of Estimation 220
10.3 Hypothesis Testing 224
10.4 Least Squares Consistent Estimation 229
11 Split Plot Models 237
11.1 A Cluster Sampling Model 238
11.2 Generalized Split Plot Models 243
11.3 The Split Plot Design 251
11.4 Identifying the Appropriate Error 254
11.5 Exercise: An Unusual Split Plot Analysis 259
12 Mixed Models and Variance Components 262
12.1 Mixed Models 263
12.2 Best Linear Unbiased Prediction 264
12.3 Mixed Model Equations 268
12.4 Variance Component Estimation: Maximum Likelihood . . 270
12.5 Maximum Likelihood Estimation for Singular Normal Dis¬
tributions 274
12.6 Variance Component Estimation: REML 275
12.7 Variance Component Estimation: MINQUE 278
12.8 Variance Component Estimation: MIVQUE 280
xvi Contents
12.9 Variance Component Estimation: Henderson s Method 3 . 281
12.10 Exact F Tests for Variance Components 285
12.10.1 Wald s Test 285
12.10.2 OfVersten s Second Method 286
12.10.3 Comparison of Tests 289
12.11 Recovery of Interblock Information in BIB Designs .... 291
12.11.1 Estimation 293
12.11.2 Model Testing 296
12.11.3 Contrasts 298
12.11.4 Alternative Inferential Procedures 299
12.11.5 Estimation of Variance Components 301
13 Checking Assumptions, Residuals, and Influential Observations 303
13.1 Leverage 306
13.1.1 Mahalanobis Distances 307
13.1.2 Diagonal Elements of the Projection Operator . . 309
13.1.3 Examples 310
13.2 Checking Normality 316
13.2.1 Other Applications for Normal Plots 321
13.3 Checking Independence 324
13.3.1 Serial Correlation 325
13.4 Heteroscedasticity and Lack of Fit 331
13.4.1 Heteroscedasticity 331
13.4.2 Lack of Fit 338
13.5 Updating Formulae and Predicted Residuals 342
13.6 Outliers and Influential Observations 346
13.7 Transformations 349
14 Variable Selection and Collinearity 352
14.1 All Possible Regressions and Best Subset Regression . . . 353
14.1.1 R2 354
14.1.2 Adjusted R2 354
14.1.3 Mallows s Cp 355
14.2 Stepwise Regression 356
14.2.1 Forward Selection 357
14.2.2 Tolerance 358
14.2.3 Backward Elimination 358
14.2.4 Other Methods 359
14.3 Discussion of Variable Selection Techniques 359
14.4 Defining Collinearity 361
14.5 Regression in Canonical Form and on Principal Components366
14.5.1 Principal Component Regression 369
14.5.2 Generalized Inverse Regression 369
14.6 Classical Ridge Regression 370
14.7 More on Mean Squared Error 371
Contents xvii
Appendix A: Vector Spaces 374
Appendix B: Matrix Results 382
B.I Basic Ideas 382
B.2 Eigenvalues and Related Results 384
B.3 Projections 389
B.4 Miscellaneous Results 397
B.5 Properties of Kronecker Products and Vec Operators . . . 399
B.6 Tensors 400
Appendix C: Some Univariate Distributions 406
Appendix D: Multivariate Distributions 410
Appendix E: Tests and Confidence Intervals 414
E.I Confidence Intervals 415
E.2 Hypothesis Testing 416
Appendix F: Equivalent Linear Models 419
F.I Constrained and Unconstrained Models 420
F.2 Estimable and Nonestimable Constraints 423
Appendix G: Randomization Theory Models 425
G.I Simple Random Sampling 426
G.2 Completely Randomized Designs 427
G.3 Randomized Complete Block Designs 429
References 433
Author Index 441
Subject Index 445
|
| any_adam_object | 1 |
| author | Christensen, Ronald 1951- |
| author_GND | (DE-588)111351820 |
| author_facet | Christensen, Ronald 1951- |
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| bvnumber | BV011002005 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279.C48 1996 |
| callnumber-search | QA279.C48 1996 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)246994861 (DE-599)BVBBV011002005 |
| dewey-full | 519.5/3520 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 20 |
| dewey-search | 519.5/35 20 |
| dewey-sort | 3519.5 235 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:26Z |
| institution | BVB |
| isbn | 0387947671 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007365663 |
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| physical | XVII, 452 S. graph. Darst. |
| publishDate | 1996 |
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| 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 2. ed. New York [u.a.] Springer 1996 XVII, 452 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Literaturverz. S. 433 - 439 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007365663&sequence=000002&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 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 | Linear models (Statistics) Analysis of variance Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Linear models (Statistics) Analysis of variance Lineares Modell Lehrbuch |
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