Theory of optimal experiments:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Pr.
1972
|
| Schriftenreihe: | Probability and mathematical statistics
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 292 S. graph. Darst. |
| ISBN: | 0122507509 |
Internformat
MARC
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| 100 | 1 | |a Fedorov, Valerij V. |e Verfasser |0 (DE-588)1047326981 |4 aut | |
| 240 | 1 | 0 | |a Teoriya optimal'nogo eksperimenta |
| 245 | 1 | 0 | |a Theory of optimal experiments |c V. V. Fedorov. Transl. and ed. by W. J. Studden and E. M. Klimko |
| 264 | 1 | |a New York [u.a.] |b Acad. Pr. |c 1972 | |
| 300 | |a XI, 292 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Probability and mathematical statistics |v 12 | |
| 650 | 4 | |a Analyse de régression | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Plan d'expérience | |
| 650 | 4 | |a Experimental design | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
| _version_ | 1804116388419207168 |
|---|---|
| adam_text | Contents
Foreword ix
Preface xi
Introduction 1
Chapter 1 —Regression Analysis and Optimality Criteria
for Regression Experiments
1.1 Basic Elements of Matrix Algebra 12
1.2 General Requirements Satisfied by Estimates 21
1.3 Best Linear Estimates 23
1.4 The Search for Estimates for Nonlinear Parametrization. Best Quasi
Linear Estimates 33
1.5 Estimation of the Dispersion of the Resulting Observations. The
Efficiency of an Experiment 36
1.6 Regression Analysis in the Presence of Errors in the Determination
of the Control Variables 40
1.7 Analysis of Experimental Data in the Case of Simultaneous Observations
of Several Variables 49
1.8 Methods of Comparing Results of Experiments 51
1.9 The Loss Function for Regression Experiments 56
1.10 The Concept of Experimental Design. Continuous Normalized Designs 58
Chapter 2—Continuous Optimal Designs
(Statistical Methods)
2.1 Basic Properties of the Information Matrix 64
2.2 Equivalence of D Optimal and Minimax Designs. Basic Properties
of These Designs 68
2.3 One Dimensional Polynomial Regression 83
2.4 Trigonometric Regression on an Interval 94
v
vi CONTENTS
2.5 Computational Methods for Construction of D Optimal Designs 97
2.6 Some Particular Iterative Procedures for Constructing D Optimal
Designs 104
2.7 Truncated D Optimal Designs 114
2.8 Nonlinear Parametrization of a Response Surface. Local D Optimal
Designs 120
2.9 Linear Criteria of Optimality 122
2.10 Iterative Methods for Constructing Linear Optimal Designs 132
2.11 Designs Minimizing TrD(e) 137
2.12 Designs Minimizing the Mean Dispersion of the Estimate of the
Response Surface over the Domain of Values 142
2.13 Extrapolation at a Point 145
2.14 Quadratic Loss 153
Chapter 3—Properties and Methods of Construction
for Optimal Discrete Designs
3.1 Discrete Designs 155
3.2 Properties and Methods of Constructing D Optimal Designs 160
3.3 Construction of Discrete Linear Optimal Designs 167
Chapter 4—Sequential Methods of Designing Experiments
for Refining and Determining Estimates
of the Parameters
4.1 Some Generalities of Contemporary Experimental Investigations 171
4.2 Sequential D Optimal Design (Linear Parametrization and Time
Constant Efficiency of the Experiment) 173
4.3 Sequential Linear Optimal Designs (Linear Parametrization and Time
Constant Efficiency of the Experiment) 183
4.4 Sequential Designs for Nonlinear Parametrization 186
4.5 Designs When the Efficiency Function of the Experiment Is Unknown 199
4.6 Design in the Presence of Errors in the Determination of
the Control Variables 202
4.7 Construction of Optimal Designs When the Experimental Conditions
Vary in Time 203
Chapter 5—Design of Experiments in the Case
of Simultaneous Observation of Several
Random Quantities
5.1 Basic Properties of the Information Matrix 209
5.2 D Optimal Designs 211
5.3 Linear Optimal Designs 221
5.4 Sequential Design 224
CONTENTS vii
Chapter 6—Discriminating Experiments
6.1 Statement of the Problem 226
6.2 Criteria Depending on the Difference of Sums of Weighted Squares
of Residuals 231
6.3 The Method of Likelihood Ratio 249
6.4 Discriminating Hypotheses Based on the Entropy Measure of Information 257
Chapter 7—Generalized Criteria of Optimality
7.1 Experiments Minimizing Generalized Loss 264
7.2 The Information Approach to the General Problem of Seeking
the True Mathematical Model 267
References 285
Subject Index 289
|
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| author | Fedorov, Valerij V. |
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| author_facet | Fedorov, Valerij V. Klimko, E. M. |
| author_role | aut |
| author_sort | Fedorov, Valerij V. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:43Z |
| institution | BVB |
| isbn | 0122507509 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001269368 |
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| physical | XI, 292 S. graph. Darst. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Acad. Pr. |
| record_format | marc |
| series | Probability and mathematical statistics |
| series2 | Probability and mathematical statistics |
| spelling | Fedorov, Valerij V. Verfasser (DE-588)1047326981 aut Teoriya optimal'nogo eksperimenta Theory of optimal experiments V. V. Fedorov. Transl. and ed. by W. J. Studden and E. M. Klimko New York [u.a.] Acad. Pr. 1972 XI, 292 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics 12 Analyse de régression Optimisation mathématique Plan d'expérience Experimental design Mathematical optimization Regression analysis Entwurf (DE-588)4121208-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Experiment (DE-588)4015999-1 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s DE-604 Statistik (DE-588)4056995-0 s Experiment (DE-588)4015999-1 s Entwurf (DE-588)4121208-3 s Studden, William J. Sonstige (DE-588)172410282 oth Klimko, E. M. edt Probability and mathematical statistics 12 (DE-604)BV000892568 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001269368&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fedorov, Valerij V. Theory of optimal experiments Probability and mathematical statistics Analyse de régression Optimisation mathématique Plan d'expérience Experimental design Mathematical optimization Regression analysis Entwurf (DE-588)4121208-3 gnd Statistik (DE-588)4056995-0 gnd Experiment (DE-588)4015999-1 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4121208-3 (DE-588)4056995-0 (DE-588)4015999-1 (DE-588)4129903-6 |
| title | Theory of optimal experiments |
| title_alt | Teoriya optimal'nogo eksperimenta |
| title_auth | Theory of optimal experiments |
| title_exact_search | Theory of optimal experiments |
| title_full | Theory of optimal experiments V. V. Fedorov. Transl. and ed. by W. J. Studden and E. M. Klimko |
| title_fullStr | Theory of optimal experiments V. V. Fedorov. Transl. and ed. by W. J. Studden and E. M. Klimko |
| title_full_unstemmed | Theory of optimal experiments V. V. Fedorov. Transl. and ed. by W. J. Studden and E. M. Klimko |
| title_short | Theory of optimal experiments |
| title_sort | theory of optimal experiments |
| topic | Analyse de régression Optimisation mathématique Plan d'expérience Experimental design Mathematical optimization Regression analysis Entwurf (DE-588)4121208-3 gnd Statistik (DE-588)4056995-0 gnd Experiment (DE-588)4015999-1 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Analyse de régression Optimisation mathématique Plan d'expérience Experimental design Mathematical optimization Regression analysis Entwurf Statistik Experiment Regressionsanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001269368&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000892568 |
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