Estimation of variance components and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland
1988
|
| Series: | North-Holland series in statistics and probability
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 370 S. |
| ISBN: | 0444700234 |
Staff View
MARC
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| 245 | 1 | 0 | |a Estimation of variance components and applications |c C. R. Rao ; J. Kleffe |
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Record in the Search Index
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| adam_text | CONTENTS
Preface v
1. Historical review v
2. Outline of the present monograph vii
References ix
Chapter 1: Matrix Algebra 1
1.1. Notation and basic results 1
1.2. Generalized inverse of matrices 3
1.3. Orthogonal projection 6
1.4. Matrix products 8
1.5. Representation of matrices by vectors 10
1.6. Quadratic subspaces 11
1.7. Quasi inner products 16
1.8. Complements and problems 22
Chapter 2: Asymptotic Distribution of Quadratic Statistics 31
2.1. Fourth order moments of quadratic statistics 31
2.2. Cumulants of quadratic forms of normal variables 36
2.3. Inequalities on moments of quadratic forms 37
2.4. Consistency of linear and quadratic functions of independent random variables 41
2.5. Asymptotic normality 47
2.6. Complements and problems 52
Chapter 3: Variance and Covariance Components Models 59
3.1. Extensions of the Gauss Markoff model 59
3.2. A general model 62
3.3. Models for two way classification data 64
3.4. Variance and covariance components 65
3.5. Autoregressive random effects 67
3.6. A general random effects model 68
3.7. A general multivariate model 69
3.8. Complements and problems 70
xii Contents
Chapter 4: Identifiability and Estimability 73
4.1. Notation 73
4.2. Identifiability 73
4.3. Unbiased estimability 75
4.4. Invariant estimability 78
4.5. Estimability of covariance parameters in growth curve models 81
4.6. Complements and problems 84
Chapter 5: Minimum Norm Quadratic Estimation 87
5.1. The principle of MINQE 87
5.2. MINQE(U. I) 93
5.3. MINQE(U) 100
5.4. ^ MINQE(U) 102
5.5. MINQE without unbiasedness 106
5.6. MINQE(U, NND) 108
5.7. Complements and problems 123
Chapter 6: Pooling of Information for Estimation 133
6.1. Replicated model 134
6.2. Models with block structure 139
6.3. Models with a common mean 143
6.4. Complements and problems 151
Chapter 7: Uniform Optimality of MINQE S 161
7.1. Uniform optimality of MINQE(U, I) 162
7.2. Uniform optimality of MINQE(U) 164
7.3. Pooled observations 167
7.4. Balanced ANOVA models 172
7.5. Complements and problems 177
Chapter 8: Computation of MINQE S for Variance Covariance
Components Models 181
8.1. The principal scheme of computations 181
8.2. Generalized hierarchical models 183
8.3. Some extensions of the algorithm 191
8.4. Nested classification model 199
8.5. Complements and problems 202
Chapter 9: Iterated MINQE and MLE 223
9.1. Iterated MINQE (IMINQE) 223
9.2. Maximum likelihood estimation (MLE) 229
9.3. Marginal MLE (MMLE) 235
Contents xiii
9.4. Computation of MLE 237
9.5. Computation of the log likelihood function 243
9.6. Complements and problems 248
Chapter 10: Asymptotic Properties of Estimators 257
10.1. Introduction 257
10.2. Consistency of MINQE 260
10.3. Asymptotic normality of MINQE(U, I) and MINQE(I) 268
10.4. Replicated error structure 272
10.5. Some results on iterated MINQE 274
10.6. Efficiency of iterated MINQE under normality 284
10.7. Large sample tests and confidence regions 288
10.8. Complements and problems 293
Chapter 11: Minimum Variance Quadratic Estimation 301
11.1. Locally best quadratic estimators 302
11.2. Bayes quadratic estimates under normal distribution 309
11.3. Hsu s theorem and extensions 317
11.4. Complements and problems 323
Chapter 12: Applications to Selection Problems 329
12.1. Selection rules 329
12.2. Simultaneous prediction in linear models 333
12.3. Simultaneous prediction in a multivariate case 341
12.4. Estimation in a mixed linear model 343
12.5. Complements and problems 348
References 351
Author Index 363
Subject Index 367
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:13Z |
| institution | BVB |
| isbn | 0444700234 |
| language | English |
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| physical | XIII, 370 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland series in statistics and probability |
| series2 | North-Holland series in statistics and probability |
| spelling | Rao, Calyampudi Radhakrishna 1920-2023 Verfasser (DE-588)119285924 aut Estimation of variance components and applications C. R. Rao ; J. Kleffe Amsterdam [u.a.] North-Holland 1988 XIII, 370 S. txt rdacontent n rdamedia nc rdacarrier North-Holland series in statistics and probability 3 Schätztheorie (DE-588)4121608-8 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 s Schätztheorie (DE-588)4121608-8 s DE-604 Kleffe, Jürgen Verfasser aut North-Holland series in statistics and probability 3 (DE-604)BV000007884 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000522987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rao, Calyampudi Radhakrishna 1920-2023 Kleffe, Jürgen Estimation of variance components and applications North-Holland series in statistics and probability Schätztheorie (DE-588)4121608-8 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| subject_GND | (DE-588)4121608-8 (DE-588)4187413-4 |
| title | Estimation of variance components and applications |
| title_auth | Estimation of variance components and applications |
| title_exact_search | Estimation of variance components and applications |
| title_full | Estimation of variance components and applications C. R. Rao ; J. Kleffe |
| title_fullStr | Estimation of variance components and applications C. R. Rao ; J. Kleffe |
| title_full_unstemmed | Estimation of variance components and applications C. R. Rao ; J. Kleffe |
| title_short | Estimation of variance components and applications |
| title_sort | estimation of variance components and applications |
| topic | Schätztheorie (DE-588)4121608-8 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| topic_facet | Schätztheorie Varianzanalyse |
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