The coordinate-free approach to linear models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2006
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
[19] |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 199 S. graph. Darst. |
| ISBN: | 0521868424 9780521868426 |
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| 245 | 1 | 0 | |a The coordinate-free approach to linear models |c Michael J. Wichura |
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| adam_text | THE COORDINATE-FREE APPROACH TO LINEAR MODELS MICHAEL J. WICHURA
CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE XI 1. INTRODUCTION 1 1.
ORIENTATION 1 2. AN ILLUSTRATIVE EXAMPLE 2 3. NOTATIONAL CONVENTIONS 4
2. TOPICS IN LINEAR ALGEBRA 6 1. ORTHOGONAL PROJECTIONS 6 2. PROPERTIES
OF ORTHOGONAL PROJECTIONS 12 2A. CHARACTERIZATION OF ORTHOGONAL
PROJECTIONS 12 2B. DIFFERENCES OF ORTHOGONAL PROJECTIONS 13 2C. SUMS OF
ORTHOGONAL PROJECTIONS 16 2D. PRODUCTS OF ORTHOGONAL PROJECTIONS 17 2E.
AN ALGEBRAIC FORM OF COCHRAN S THEOREM 19 3. TJUR S THEOREM 21 4.
SELF-ADJOINT TRANSFORMATIONS AND THE SPECTRAL THEOREM 32 5.
REPRESENTATION OF LINEAR AND BILINEAR FUNCTIONALS 36 6. PROBLEM SET:
CLEVELAND S IDENTITY 40 7. APPENDIX: RUDIMENTS 41 7A. VECTOR SPACES . .
. . 42 7B. SUBSPACES 43 7C. LINEAR FUNCTIONALS 43 7D. LINEAR
TRANSFORMATIONS 43 3. RANDOM VECTORS 45 1. RANDOM VECTORS TAKING VALUES
IN AN INNER PRODUCT SPACE . . . . 45 2. EXPECTED VALUES 46 : 3.
COVARIANCE OPERATORS 47 4. DISPERSION OPERATORS 49 5. WEAK SPHERICITY 51
6. GETTING TO WEAK SPHERICITY 52 7. NORMALITY 52 8. THE MAIN RESULT 54
9. PROBLEM SET: DISTRIBUTION OF QUADRATIC FORMS 57 VIII CONTENTS 4.
GAUSS-MARKOV ESTIMATION 60 1 . LINEAR FUNCTIONALS OF /I 60 2. ESTIMATION
OF LINEAR FUNCTIONALS OF /I 62 3. ESTIMATION OF I ITSELF 67 4.
ESTIMATION OF IT 2 70 5. USING THE WRONG INNER PRODUCT 72 6. INVARIANCE
OF GMES UNDER LINEAR TRANSFORMATIONS 74 7. SOME ADDITIONAL OPTIMALITY
PROPERTIES OF GMES 75 8. ESTIMABLE PARAMETRIC FUNCTIONALS 78 9. PROBLEM
SET: QUANTIFYING THE GAUSS-MARKOV THEOREM 85 5. NORMAL THEORY:
ESTIMATION 89 1. MAXIMUM LIKELIHOOD ESTIMATION 89 2. MINIMUM VARIANCE
UNBIASED ESTIMATION 90 3. MINIMAXITY OF PM Y 92 4. JAMES-STEIN
ESTIMATION 97 5. PROBLEM SET: ADMISSIBLE MINIMAX ESTIMATION OF /I 104 6.
NORMAL THEORY: TESTING 110 1. THE LIKELIHOOD RATIO TEST ILL 2. THE
F-TEST 112 3. MONOTONICITY OF THE POWER OF THE F-TEST 117 4. AN OPTIMAL
PROPERTY OF THE F-TEST 121 5. CONFIDENCE INTERVALS FOR LINEAR
FUNCTIONALS OF FJ, 127 6. PROBLEM SET: WALD S THEOREM 136 7. ANALYSIS OF
COVARIANCE 141 1. PRELIMINARIES ON NONORTHOGONAL PROJECTIONS 141 1A.
CHARACTERIZATION OF PROJECTIONS 142 IB. THE ADJOINT OF A PROJECTION 142
1C. AN ISOMORPHISM BETWEEN J AND I 1 - 143 ID. A FORMULA FOR PJJ WHEN J
IS GIVEN BY A BASIS . . . ... . 143 IE. A FORMULA FOR P J.J WHEN J IS
GIVEN BY A BASIS 145 2. THE ANALYSIS OF COVARIANCE FRAMEWORK 146 3.
GAUSS-MARKOV ESTIMATION 147 4. VARIANCES AND COVARIANCES OF GMES 150 5.
ESTIMATION OF A 2 152 6. SCHEFFE INTERVALS FOR FUNCTIONALS OF HM 153 7.
F-TESTING 155 8. PROBLEM SET: THE LATIN SQUARE DESIGN 159 8. MISSING
OBSERVATIONS 164 1. FRAMEWORK AND GAUSS-MARKOV ESTIMATION 164 2.
OBTAINING FI 169 2A. THE CONSISTENCY EQUATION METHOD 169 2B. THE
QUADRATIC FUNCTION METHOD 172 2C. THE ANALYSIS OF COVARIANCE METHOD 173
CONTENTS IX 3. ESTIMATION OF A 2 176 4. F-TESTING 177 5. ESTIMATION OF
LINEAR FUNCTIONALS 181 6. PROBLEM SET: EXTRA OBSERVATIONS 184 REFERENCES
188 INDEX 190
|
| adam_txt |
THE COORDINATE-FREE APPROACH TO LINEAR MODELS MICHAEL J. WICHURA
CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE XI 1. INTRODUCTION 1 1.
ORIENTATION 1 2. AN ILLUSTRATIVE EXAMPLE 2 3. NOTATIONAL CONVENTIONS 4
2. TOPICS IN LINEAR ALGEBRA 6 1. ORTHOGONAL PROJECTIONS 6 2. PROPERTIES
OF ORTHOGONAL PROJECTIONS 12 2A. CHARACTERIZATION OF ORTHOGONAL
PROJECTIONS 12 2B. DIFFERENCES OF ORTHOGONAL PROJECTIONS 13 2C. SUMS OF
ORTHOGONAL PROJECTIONS 16 2D. PRODUCTS OF ORTHOGONAL PROJECTIONS 17 2E.
AN ALGEBRAIC FORM OF COCHRAN'S THEOREM 19 3. TJUR'S THEOREM 21 4.
SELF-ADJOINT TRANSFORMATIONS AND THE SPECTRAL THEOREM 32 5.
REPRESENTATION OF LINEAR AND BILINEAR FUNCTIONALS 36 6. PROBLEM SET:
CLEVELAND'S IDENTITY 40 7. APPENDIX: RUDIMENTS 41 7A. VECTOR SPACES . .
. . 42 7B. SUBSPACES 43 7C. LINEAR FUNCTIONALS 43 7D. LINEAR
TRANSFORMATIONS 43 3. RANDOM VECTORS 45 1. RANDOM VECTORS TAKING VALUES
IN AN INNER PRODUCT SPACE . . . . 45 2. EXPECTED VALUES 46 : 3.
COVARIANCE OPERATORS 47 4. DISPERSION OPERATORS 49 5. WEAK SPHERICITY 51
6. GETTING TO WEAK SPHERICITY 52 7. NORMALITY 52 8. THE MAIN RESULT 54
9. PROBLEM SET: DISTRIBUTION OF QUADRATIC FORMS 57 VIII CONTENTS 4.
GAUSS-MARKOV ESTIMATION 60 1 . LINEAR FUNCTIONALS OF /I 60 2. ESTIMATION
OF LINEAR FUNCTIONALS OF /I 62 3. ESTIMATION OF \I ITSELF 67 4.
ESTIMATION OF IT 2 70 5. USING THE WRONG INNER PRODUCT 72 6. INVARIANCE
OF GMES UNDER LINEAR TRANSFORMATIONS 74 7. SOME ADDITIONAL OPTIMALITY
PROPERTIES OF GMES 75 8. ESTIMABLE PARAMETRIC FUNCTIONALS 78 9. PROBLEM
SET: QUANTIFYING THE GAUSS-MARKOV THEOREM 85 5. NORMAL THEORY:
ESTIMATION 89 1. MAXIMUM LIKELIHOOD ESTIMATION 89 2. MINIMUM VARIANCE
UNBIASED ESTIMATION 90 3. MINIMAXITY OF PM Y 92 4. JAMES-STEIN
ESTIMATION 97 5. PROBLEM SET: ADMISSIBLE MINIMAX ESTIMATION OF /I 104 6.
NORMAL THEORY: TESTING 110 1. THE LIKELIHOOD RATIO TEST ILL 2. THE
F-TEST 112 3. MONOTONICITY OF THE POWER OF THE F-TEST 117 4. AN OPTIMAL
PROPERTY OF THE F-TEST 121 5. CONFIDENCE INTERVALS FOR LINEAR
FUNCTIONALS OF FJ, 127 6. PROBLEM SET: WALD'S THEOREM 136 7. ANALYSIS OF
COVARIANCE 141 1. PRELIMINARIES ON NONORTHOGONAL PROJECTIONS 141 1A.
CHARACTERIZATION OF PROJECTIONS 142 IB. THE ADJOINT OF A PROJECTION 142
1C. AN ISOMORPHISM BETWEEN J AND I 1 - 143 ID. A FORMULA FOR PJJ WHEN J
IS GIVEN BY A BASIS . . . . . 143 IE. A FORMULA FOR P'J.J WHEN J IS
GIVEN BY A BASIS 145 2. THE ANALYSIS OF COVARIANCE FRAMEWORK 146 3.
GAUSS-MARKOV ESTIMATION 147 4. VARIANCES AND COVARIANCES OF GMES 150 5.
ESTIMATION OF A 2 152 6. SCHEFFE INTERVALS FOR FUNCTIONALS OF HM 153 7.
F-TESTING 155 8. PROBLEM SET: THE LATIN SQUARE DESIGN 159 8. MISSING
OBSERVATIONS 164 1. FRAMEWORK AND GAUSS-MARKOV ESTIMATION 164 2.
OBTAINING FI 169 2A. THE CONSISTENCY EQUATION METHOD 169 2B. THE
QUADRATIC FUNCTION METHOD 172 2C. THE ANALYSIS OF COVARIANCE METHOD 173
CONTENTS IX 3. ESTIMATION OF A 2 176 4. F-TESTING 177 5. ESTIMATION OF
LINEAR FUNCTIONALS 181 6. PROBLEM SET: EXTRA OBSERVATIONS 184 REFERENCES
188 INDEX 190 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:22:28Z |
| indexdate | 2024-07-09T20:52:07Z |
| institution | BVB |
| isbn | 0521868424 9780521868426 |
| language | English |
| lccn | 2006004133 |
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| physical | XIII, 199 S. graph. Darst. |
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| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Wichura, Michael J. Verfasser aut The coordinate-free approach to linear models Michael J. Wichura 1. publ. Cambridge [u.a.] Cambridge University Press 2006 XIII, 199 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [19] Includes bibliographical references and index Modelos lineares larpcal Linear models (Statistics) Analysis of variance Regression analysis Analysis of covariance Lineares Modell (DE-588)4134827-8 gnd rswk-swf Kovarianzanalyse (DE-588)4197017-2 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s Regressionsanalyse (DE-588)4129903-6 s Varianzanalyse (DE-588)4187413-4 s Kovarianzanalyse (DE-588)4197017-2 s b DE-604 Cambridge series in statistical and probabilistic mathematics [19] (DE-604)BV011442366 19 http://www.loc.gov/catdir/toc/ecip068/2006004133.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0642/2006004133-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015406223&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wichura, Michael J. The coordinate-free approach to linear models Cambridge series in statistical and probabilistic mathematics Modelos lineares larpcal Linear models (Statistics) Analysis of variance Regression analysis Analysis of covariance Lineares Modell (DE-588)4134827-8 gnd Kovarianzanalyse (DE-588)4197017-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4197017-2 (DE-588)4129903-6 (DE-588)4187413-4 |
| title | The coordinate-free approach to linear models |
| title_auth | The coordinate-free approach to linear models |
| title_exact_search | The coordinate-free approach to linear models |
| title_exact_search_txtP | The coordinate-free approach to linear models |
| title_full | The coordinate-free approach to linear models Michael J. Wichura |
| title_fullStr | The coordinate-free approach to linear models Michael J. Wichura |
| title_full_unstemmed | The coordinate-free approach to linear models Michael J. Wichura |
| title_short | The coordinate-free approach to linear models |
| title_sort | the coordinate free approach to linear models |
| topic | Modelos lineares larpcal Linear models (Statistics) Analysis of variance Regression analysis Analysis of covariance Lineares Modell (DE-588)4134827-8 gnd Kovarianzanalyse (DE-588)4197017-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| topic_facet | Modelos lineares Linear models (Statistics) Analysis of variance Regression analysis Analysis of covariance Lineares Modell Kovarianzanalyse Regressionsanalyse Varianzanalyse |
| url | http://www.loc.gov/catdir/toc/ecip068/2006004133.html http://www.loc.gov/catdir/enhancements/fy0642/2006004133-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015406223&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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