A course in linear models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1983
|
| Schriftenreihe: | Statistics: textbooks and monographs
volume 45 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 422 S. |
| ISBN: | 0824715853 |
Internformat
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| 100 | 1 | |a Kshirsagar, Anant M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A course in linear models |c Anant M. Kshirsagar |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1983 | |
| 300 | |a XVI, 422 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Statistics: textbooks and monographs |v volume 45 | |
| 650 | 7 | |a Statistical Methods |2 cabt | |
| 650 | 7 | |a Lineaire modellen |2 gtt | |
| 650 | 4 | |a Modèles linéaires (Statistique) | |
| 650 | 7 | |a Statistiek |2 gtt | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Linear models (Statistics) | |
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Datensatz im Suchindex
| _version_ | 1804116728402149376 |
|---|---|
| adam_text | CONTENTS
PREFACE v
NOTATION AND ABBREVIATIONS
CHAPTER 1. LINEAR MODELS 1
1. Introduction 1
2. Relationship of One Variable with Others 3
3. Some Results About Vectors and Matrices 5
4. Variance—Covariance Matrix 10
CHAPTER 2. THE GENERAL LINEAR MODEL 13
1. Introduction 13
2. A Generalized Inverse of a Matrix 17
3. Solution of the Normal Equations 22
4. Estimability of a Linear Parametric Function 25
5. The Gauss Markoff Theorem 27
6. Variances and Covariances of BLUES 29
7. Estimation Space 32
8. Error Space 34
9. Spectral Decomposition of the Matrix S 39
10. Projection on the Estimation Space 41
11. Additional Equations to Solve the Normal Equations 43
12. Reduced Normal Equations 43
13. Illustrative Examples and Additional Results 45
Exercises
ix
x Contents
CHAPTER 3. INTERVAL ESTIMATES AND TESTS OF HYPOTHESES 69
1. Distribution of the Error S.S. and
Other Distributions 69
2. Conditional Error S.S. 74
3. Distribution of the Regression S.S. 78
4. Tests of Hypotheses About Estimable
Parametric Functions 80
5. Power of the Test 84
6. Confidence Intervals 86
7. Regression S.S. 87
8. Quadratic Forms in Idempotent Matrices 90
9. Distribution and Independence of Quadratic Forms 92
10. Illustrative Examples 96
Appendix to Chapter 3 110
Exercises 115
CHAPTER 4. MULTIPLE REGRESSION 119
1. Regression 119
2. Analysis of the Multiple Regression Model 121
3. Testing a Subhypothesis 130
4. Orthogonality 136
5. Curvilinear Regression 138
6. Orthogonal Polynomials 139
7. Response Surface Methodology 142
8. Discriminant Analysis 144
9. Illustrative Examples 145
Exercises 157
CHAPTER 5. ANALYSIS OF VARIANCE 161
1. Introduction 161
2. Analysis of Variance for a One Way
Classification Model 162
3. Sums of Squares as Quadratic Forms in
Idempotent Matrices 175
4. Breakdown of the Between Groups S.S. 179
5. Power of the Analysis of Variance Test 181
6. Illustrative Examples 184
Exercises 192
Contents xi
CHAPTER 6. COMPARISON OF INDIVIDUAL MEANS 195
1. Introduction 195
2. Error Rates 196
3. Fisher s LSD Methods 197
4. Tukey s Method 198
5. Newman Keul s Multiple Range Test 199
6. Tukey s Multiple Range Method 200
7. Scheffe s Method 200
8. Duncan s Multiple Range Test 201
9. Bonferroni t Statistics 201
10. Miscellaneous Remarks 203
11. Illustrative Examples 204
Exercises 206
CHAPTER 7. ANALYSIS OF VARIANCE (MULTI WAY CLASSIFICATION) 209
1. Analysis of Variance: Two Way Classification 209
2. Analysis of the Data 211
3. Tests of Hypotheses Associated with ex s and g s 215
4. Orthogonality of a s and g s 218
5. Two Way Classification; One Observation Per Cell,
Interaction Present 220
6. Two Way Classification with Interaction and
R Observations Per Cell 226
7. Representation of Sums of Squares as Quadratic
Forms in the Vector of Observations 234
8. Tukey s Test for Non Additivity, with 1 d.f. 236
9. Extensions of Tukey s Test 243
10. Three Way and Multi Way Classifications 246
11. Nested Models 256
12. Illustrative Examples 261
Exercises 267
CHAPTER 8. ANALYSIS OF VARIANCE—TWO WAY CLASSIFICATION,
WITH UNEQUAL NUMBER OF OBSERVATIONS PER CELL 271
1. Model Without Interaction 271
2. Estimable Parametric Functions and Their BLUES 278
3. Tests of Hypotheses 282
4. The Particular Case of Proportional Frequencies 287
xii Contents
5. Analysis When the Sank of C is Less Than p 1 289
6. Two Way Classification, with Interaction and
Unequal (But Non Zero) Numbers of Observations
Per Cell 290
7. Illustrative Examples 299
CHAPTER 9. ANALYSIS OF COVARIANCE 311
1. Introduction 311
2. Analysis of Covarxance
3. Analysis of Covarxance of a Two Way Classification
4. Adjusted Row Means
5. Additional Material Related to Analysis
of Covarxance
Exercises
CHAPTER 10. METHOD OF GENERALIZED LEAST SQUARES 333
1. Introduction 333
2. Generalized Least Squares 334
3. Application in Sampling From a Finite Population 338
4. Combination of Estimates of a Parameter 0 341
5. Two Way Classification 342
6. Estimation of Location and Scale Parameters 342
Exercises 345
CHAPTER 11. MISSING PLOTS TECHNIQUE AND MISCELLANEOUS TOPICS 351
1. Missing Observations 351
2. Two Way Classification, With One Missing Observation 354
3. S.S. for Testing a Linear Hypotheses, In Case
of Missing Data 357
4. The Value f* of f_, That Minimizes the Error S.S. 361
5. Loss of Efficiency Due to Missing Values 363
6. Computational Procedure for the Analysis of Data
From a Linear Model, With Missing Observations 365
7. Use of Analysis of Covariance 366
8. Illustrative Examples 368
9. Miscellaneous Topics in Linear Models 372
Exercises 373
Contents xiii
CHAPTER 12. VARIANCE COMPONENTS ANALYSIS 377
1. Introduction 377
2. One Way Classification (Equal Number
of Observations) 378
3. One Way Classification (Unequal Number
of Observations) 384
4. Multi Way Classification With Equal Number
of Observations in Cells 385
5. Distribution Under Assumption of Normality 389
6. Hartley s Method of Synthesis 395
7. MINQUE Method 398
8. Miscellaneous Topics 403
9. Illustrative Examples 404
Exercises 406
REFERENCES 411
AUTHOR INDEX 417
SUBJECT INDEX 419
|
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| classification_tum | MAT 628f |
| ctrlnum | (OCoLC)9018243 (DE-599)BVBBV002270641 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-07-09T15:43:07Z |
| institution | BVB |
| isbn | 0824715853 |
| language | English |
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| spelling | Kshirsagar, Anant M. Verfasser aut A course in linear models Anant M. Kshirsagar New York [u.a.] Dekker 1983 XVI, 422 S. txt rdacontent n rdamedia nc rdacarrier Statistics: textbooks and monographs volume 45 Statistical Methods cabt Lineaire modellen gtt Modèles linéaires (Statistique) Statistiek gtt Statistik Linear models (Statistics) Statistik (DE-588)4056995-0 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s DE-604 Statistik (DE-588)4056995-0 s Statistics textbooks and monographs 45 (DE-604)BV000003265 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001491946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kshirsagar, Anant M. A course in linear models Statistical Methods cabt Lineaire modellen gtt Modèles linéaires (Statistique) Statistiek gtt Statistik Linear models (Statistics) Statistik (DE-588)4056995-0 gnd Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4134827-8 |
| title | A course in linear models |
| title_auth | A course in linear models |
| title_exact_search | A course in linear models |
| title_full | A course in linear models Anant M. Kshirsagar |
| title_fullStr | A course in linear models Anant M. Kshirsagar |
| title_full_unstemmed | A course in linear models Anant M. Kshirsagar |
| title_short | A course in linear models |
| title_sort | a course in linear models |
| topic | Statistical Methods cabt Lineaire modellen gtt Modèles linéaires (Statistique) Statistiek gtt Statistik Linear models (Statistics) Statistik (DE-588)4056995-0 gnd Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Statistical Methods Lineaire modellen Modèles linéaires (Statistique) Statistiek Statistik Linear models (Statistics) Lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001491946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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