Holdings: Parameter estimation for scientists and engineers

Parameter estimation for scientists and engineers:

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Bibliographic Details
Main Author:	Bos, Adriaan van den (Author)
Format:	Book
Language:	English
Published:	Hoboken, NJ Wiley-Interscience 2007
Subjects:	Estimation d'un paramètre Estimation, Théorie de l' Ingénierie - Méthodes statistiques Statistique mathématique Ingenieurwissenschaften Engineering > Statistical methods Parameter estimation Parameteridentifikation Numerisches Verfahren Parameter > Mathematik
Online Access:	Table of contents only Publisher description Contributor biographical information Inhaltsverzeichnis
Item Description:	Includes bibliographical references (p. 269-270) and index
Physical Description:	XIV, 273 S. graph. Darst.
ISBN:	0470147814 9780470147818

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adam_text	PARAMETER ESTIMATION FOR SCIENTISTS AND ENGINEERS ADRIAAN VAN DEN BOS IICENTENNIAL B1CENTENNIAL WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS PREFACE XIII 1 INTRODUCTION 1 2 PARAMETRIC MODEIS OF OBSERVATIONS 7 2.1 INTRODUCTION 7 2.2 PURPOSES OF MODEL PARAMETER ESTIMATION 8 2.3 TRADITIONAL DETERMINISTIC PARAMETER ESTIMATION METHODS 9 2.4 STATISTICAL PARAMETRIC MODEIS OF OBSERVATIONS 12 2.4.1 THE EXPECTATION MODEL 12 2.4.2 ADVANTAGES OF STATISTICAL PARAMETRIC MODEIS OF OBSERVATIONS 16 2.5 CONCLUSIONS 20 2.6 COMMENTS AND REFERENCES 20 3 DISTRIBUTIONS OF OBSERVATIONS 21 3.1 INTRODUCTION 21 3.2 EXPECTATION, COVARIANCE, AND FISHER SCORE 21 3.3 THE JOINT REAL NORMAL DISTRIBUTION 24 3.3.1 THE JOINT REAL NORMAL PROBABILITY DENSITY FUNCTION 24 3.3.2 THE FISHER SCORE OF NORMAL OBSERVATIONS 25 VII VIII CONTENTS 3.4 THE POISSON DISTRIBUTION 25 3.4.1 THE POISSON PROBABILITY FUNCTION 25 3.4.2 THE FISHER SCORE OF POISSON OBSERVATIONS 26 3.5 THE MULTINOMIAL DISTRIBUTION 27 3.5.1 THE MULTINOMIAL PROBABILITY FUNCTION 27 3.5.2 THE FISHER SCORE OF MULTINOMIAL OBSERVATIONS 29 3.6 EXPONENTIAL FAMILIES OF DISTRIBUTIONS 30 3.6.1 DEFINITION AND EXAMPLES 30 3.6.2 PROPERTIES OF EXPONENTIAL FAMILIES OF DISTRIBUTIONS 32 3.7 STATISTICAL PROPERTIES OF FISHER SCORES 35 3.8 COMPLEX STOCHASTIC VARIABLES 37 3.8.1 SCALAR COMPLEX STOCHASTIC VARIABLES 37 3.8.2 VECTORS OF COMPLEX STOCHASTIC VARIABLES 38 3.8.3 VECTORS OF REAL AND COMPLEX STOCHASTIC VARIABLES 39 3.9 THE JOINT REAL-COMPLEX NORMAL DISTRIBUTION 40 3.10 COMMENTS AND REFERENCES 41 3.11 PROBLEMS 42 PRECISION AND ACCURACY 45 4.1 INTRODUCTION 45 4.2 PROPERTIES OF ESTIMATORS 46 4.3 PROPERTIES OF COVARIANCE MATRICES 48 4.3.1 REAL COVARIANCE MATRICES 48 4.3.2 COMPLEX COVARIANCE MATRICES 50 4.4 FISHER INFORMATION 51 4.4.1 DEFINITION OF THE FISHER INFORMATION MATRIX 51 4.4.2 THE FISHER INFORMATION MATRIX FOR EXPONENTIAL FAMILIES OF DISTRIBUTIONS 55 4.4.3 INFLOW OF FISHER INFORMATION 56 4.5 LIMITS TO PRECISION: THE CRAMER-RAO LOWER BOUND 60 4.5.1 THE CRAMER-RAO LOWER BOUND FOR SCALAR FUNCTIONS OF SCALAR PARAMETERS 60 4.5.2 THE CRAMER-RAO LOWER BOUND FOR VECTOR FUNCTIONS OF VECTOR PARAMETERS 63 4.6 PROPERTIES OF THE CRAMER-RAO LOWER BOUND 66 4.6.1 INTERPRETATION OF THE EXPRESSION FOR THE CRAMER-RAO LOWER BOUND 66 4.6.2 THE CRAMER-RAO LOWER BOUND AS A MEASURE OF EFFICIENCY OF ESTIMATION 67 4.6.3 MONOTONICITY WITH THE NUMBER OF OBSERVATIONS 70 4.6.4 PROPAGATION OF STANDARD DEVIATION 70 4.6.5 INFLUENCE OF ESTIMATION OF ADDITIONAL PARAMETERS 71 4.6.6 THE CRAMER-RAO LOWER BOUND FOR BIASED ESTIMATORS 72 CONTENTS IX 4.7 THE CRAMER-RAO LOWER BOUND FOR COMPLEX PARAMETERS OR FUNCTIONS OF PARAMETERS 74 4.7.1 INTRODUCTION 74 4.7.2 THE CRAMER-RAO LOWER BOUND FOR VECTORS OF REAL AND COMPLEX FUNCTIONS OF REAL PARAMETERS 75 4.7.3 THE CRAMER-RAO LOWER BOUND FOR VECTORS OF REAL AND COMPLEX FUNCTIONS OF REAL AND COMPLEX PARAMETERS 76 4.8 THE CRAMER-RAO LOWER BOUND FOR EXPONENTIAL FAMILIES OF DISTRIBUTIONS 78 4.9 THE CRAMER-RAO LOWER BOUND AND IDENTINABILITY 79 4.10 THE CRAMER-RAO LOWER BOUND AND EXPERIMENTAL DESIGN 81 4.10.1 INTRODUCTION 81 4.10.2 EXPERIMENTAL DESIGN FOR NONLINEAR VECTOR PARAMETERS 84 4.11 COMMENTS AND REFERENCES 91 4.12 PROBLEMS 91 5 PRECISE AND ACCURATE ESTIMATION 99 5.1 INTRODUCTION 99 5.2 MAXIMUM LIKELIHOOD ESTIMATION 100 5.3 PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS 105 5.3.1 THE INVARIANCE PROPERTY OF MAXIMUM LIKELIHOOD ESTIMATORS 105 5.3.2 CONNECTION OF EFFICIENT UNBIASED ESTIMATORS AND MAXIMUM LIKELIHOOD ESTIMATORS 106 5.3.3 CONSISTENCY OF MAXIMUM LIKELIHOOD ESTIMATORS 106 5.3.4 ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS 110 5.3.5 ASYMPTOTIC EFFICIENCY OF MAXIMUM LIKELIHOOD ESTIMATORS 112 5.4 MAXIMUM LIKELIHOOD FOR NORMALLY DISTRIBUTED OBSERVATIONS 113 5.4.1 THE LIKELIHOOD FUNCTION FOR NORMALLY DISTRIBUTED OBSERVATIONS 113 5.4.2 PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS FOR NORMALLY DISTRIBUTED OBSERVATIONS 115 5.4.3 MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF LINEAR MODEIS FROM NORMALLY DISTRIBUTED OBSERVATIONS 121 5.5 MAXIMUM LIKELIHOOD FOR POISSON DISTRIBUTED OBSERVATIONS 123 5.6 MAXIMUM LIKELIHOOD FOR MULTINOMIALLY DISTRIBUTED OBSERVATIONS 124 5.7 MAXIMUM LIKELIHOOD FOR EXPONENTIAL FAMILY DISTRIBUTED OBSERVATIONS 125 5.8 TESTING THE EXPECTATION MODEL: THE LIKELIHOOD RATIO TEST 126 5.8.1 MODEL TESTING FOR ARBITRARY DISTRIBUTIONS 126 5.8.2 MODEL TESTING FOR EXPONENTIAL FAMILIES OF DISTRIBUTIONS 132 5.9 LEAST SQUARES ESTIMATION 134 5.10 NONLINEAR LEAST SQUARES ESTIMATION 136 5.11 LINEAR LEAST SQUARES ESTIMATION 139 5.12 WEIGHTED LINEAR LEAST SQUARES ESTIMATION 140 5.13 PROPERTIES OF THE LINEAR LEAST SQUARES ESTIMATOR 144 X CONTENTS 5.14 THE BEST LINEAR UNBIASED ESTIMATOR 145 5.15 SPECIAL CASES OF THE BEST LINEAR UNBIASED ESTIMATOR AND A RELATED RESULT 147 5.15.1 THE GAUSS-MARKOV THEOREM 147 5.15.2 NORMALLY DISTRIBUTED OBSERVATIONS 148 5.15.3 EXPONENTIAL FAMILY DISTRIBUTED OBSERVATIONS 148 5.16 COMPLEX LINEAR LEAST SQUARES ESTIMATION 149 5.17 SUMMARY OF PROPERTIES OF LINEAR LEAST SQUARES ESTIMATORS 151 5.18 RECURSIVE LINEAR LEAST SQUARES ESTIMATION 152 5.19 RECURSIVE LINEAR LEAST SQUARES ESTIMATION WITH FORGETTING 155 5.20 COMMENTS AND REFERENCES 157 5.21 PROBLEMS 158 NUMERICAL METHODS FOR PARAMETER ESTIMATION 163 6.1 INTRODUCTION 163 6.2 NUMERICAL OPTIMIZATION 164 6.2.1 KEY NOTIONS IN NUMERICAL OPTIMIZATION 164 6.2.2 REFERENCE LOG-LIKELIHOOD FUNCTIONS AND LEAST SQUARES CRITERIA 166 6.3 THE STEEPEST DESCENT METHOD 168 6.3.1 DEFINITION OF THE STEEPEST DESCENT STEP 168 6.3.2 PROPERTIES OF THE STEEPEST DESCENT STEP 171 6.4 THE NEWTON METHOD 174 6.4.1 DEFINITION OF THE NEWTON STEP 174 6.4.2 PROPERTIES OF THE NEWTON STEP 175 6.4.3 THE NEWTON STEP FOR MAXIMIZING LOG-LIKELIHOOD FUNCTIONS 182 6.5 THE FISHER SCORING METHOD 183 6.5.1 DEFINITION OF THE FISHER SCORING STEP 183 6.5.2 PROPERTIES OF THE FISHER SCORING STEP 183 6.5.3 FISHER SCORING STEP FOR EXPONENTIAL FAMILIES 185 6.6 THE NEWTON METHOD FOR NORMAL MAXIMUM LIKELIHOOD AND FOR NONLINEAR LEAST SQUARES 185 6.6.1 THE NEWTON STEP FOR NORMAL MAXIMUM LIKELIHOOD 185 6.6.2 THE NEWTON STEP FOR NONLINEAR LEAST SQUARES 187 6.7 THE GAUSS-NEWTON METHOD 188 6.7.1 DEFINITION OF THE GAUSS-NEWTON STEP 188 6.7.2 PROPERTIES OF THE GAUSS-NEWTON STEP 188 6.8 THE NEWTON METHOD FOR POISSON MAXIMUM LIKELIHOOD 191 6.9 THE NEWTON METHOD FOR MULTINOMIAL MAXIMUM LIKELIHOOD 192 6.10 THE NEWTON METHOD FOR EXPONENTIAL FAMILY MAXIMUM LIKELIHOOD 193 6.11 THE GENERALIZED GAUSS-NEWTON METHOD FOR EXPONENTIAL FAMILY MAXIMUM LIKELIHOOD 194 6.11.1 DEFINITION OF THE GENERALIZED GAUSS-NEWTON STEP 194 6.11.2 PROPERTIES OF THE GENERALIZED GAUSS-NEWTON METHOD 195 CONTENTS XI 6.12 THE ITERATIVELY REWEIGHTED LEAST SQUARES METHOD 197 6.13 THE LEVENBERG-MARQUARDT METHOD 197 6.13.1 DEFINITION OF THE LEVENBERG-MARQUARDT STEP 197 6.13.2 PROPERTIES OF THE LEVENBERG-MARQUARDT STEP 199 6.14 SUMMARY OF THE DESCRIBED NUMERICAL OPTIMIZATION METHODS 200 6.14.1 INTRODUCTION 200 6.14.2 THE STEEPEST ASCENT (DESCENT) METHOD 200 6.14.3 THE NEWTON METHOD 200 6.14.4 THE FISHER SCORING METHOD 201 6.14.5 THE GAUSS-NEWTON METHOD 201 6.14.6 THE GENERALIZED GAUSS-NEWTON METHOD 202 6.14.7 THE ITERATIVELY REWEIGHTED LEAST SQUARES METHOD 202 6.14.8 THE LEVENBERG-MARQUARDT METHOD 202 6.14.9 CONCLUSIONS 202 6.15 PARAMETER ESTIMATION METHODOLOGY 203 6.15.1 INTRODUCTION 203 6.15.2 INVESTIGATING THE FEASIBILITY OF THE OBSERVATIONS 203 6.15.3 PRELIMINARY SIMULATION EXPERIMENTS 204 6.16 COMMENTS AND REFERENCES 206 6.17 PROBLEMS 206 7 SOLUTIONS OR PARTIAL SOLUTIONS TO PROBLEMS 211 APPENDIX A: STATISTICAL RESULTS 247 A. 1 STATISTICAL PROPERTIES OF LINEAR COMBINATIONS OF STOCHASTIC VARIABLES 247 A.2 THE CAUCHY-SCHWARZ INEQUALITY FOR EXPECTATIONS 249 APPENDIX B: VECTORS AND MATRICES 251 B.L VECTORS 251 B.2 MATRICES 252 APPENDIX C: POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES 259 C.L REAL POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES 259 C.2 COMPLEX POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES 263 APPENDIX D: VECTOR AND MATRIX DIFFERENTIATION 265 REFERENCES 269 TOPIC INDEX 271
adam_txt	PARAMETER ESTIMATION FOR SCIENTISTS AND ENGINEERS ADRIAAN VAN DEN BOS IICENTENNIAL B1CENTENNIAL WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS PREFACE XIII 1 INTRODUCTION 1 2 PARAMETRIC MODEIS OF OBSERVATIONS 7 2.1 INTRODUCTION 7 2.2 PURPOSES OF MODEL PARAMETER ESTIMATION 8 2.3 TRADITIONAL DETERMINISTIC PARAMETER ESTIMATION METHODS 9 2.4 STATISTICAL PARAMETRIC MODEIS OF OBSERVATIONS 12 2.4.1 THE EXPECTATION MODEL 12 2.4.2 ADVANTAGES OF STATISTICAL PARAMETRIC MODEIS OF OBSERVATIONS 16 2.5 CONCLUSIONS 20 2.6 COMMENTS AND REFERENCES 20 3 DISTRIBUTIONS OF OBSERVATIONS 21 3.1 INTRODUCTION 21 3.2 EXPECTATION, COVARIANCE, AND FISHER SCORE 21 3.3 THE JOINT REAL NORMAL DISTRIBUTION 24 3.3.1 THE JOINT REAL NORMAL PROBABILITY DENSITY FUNCTION 24 3.3.2 THE FISHER SCORE OF NORMAL OBSERVATIONS 25 VII VIII CONTENTS 3.4 THE POISSON DISTRIBUTION 25 3.4.1 THE POISSON PROBABILITY FUNCTION 25 3.4.2 THE FISHER SCORE OF POISSON OBSERVATIONS 26 3.5 THE MULTINOMIAL DISTRIBUTION 27 3.5.1 THE MULTINOMIAL PROBABILITY FUNCTION 27 3.5.2 THE FISHER SCORE OF MULTINOMIAL OBSERVATIONS 29 3.6 EXPONENTIAL FAMILIES OF DISTRIBUTIONS 30 3.6.1 DEFINITION AND EXAMPLES 30 3.6.2 PROPERTIES OF EXPONENTIAL FAMILIES OF DISTRIBUTIONS 32 3.7 STATISTICAL PROPERTIES OF FISHER SCORES 35 3.8 COMPLEX STOCHASTIC VARIABLES 37 3.8.1 SCALAR COMPLEX STOCHASTIC VARIABLES 37 3.8.2 VECTORS OF COMPLEX STOCHASTIC VARIABLES 38 3.8.3 VECTORS OF REAL AND COMPLEX STOCHASTIC VARIABLES 39 3.9 THE JOINT REAL-COMPLEX NORMAL DISTRIBUTION 40 3.10 COMMENTS AND REFERENCES 41 3.11 PROBLEMS 42 PRECISION AND ACCURACY 45 4.1 INTRODUCTION 45 4.2 PROPERTIES OF ESTIMATORS 46 4.3 PROPERTIES OF COVARIANCE MATRICES 48 4.3.1 REAL COVARIANCE MATRICES 48 4.3.2 COMPLEX COVARIANCE MATRICES 50 4.4 FISHER INFORMATION 51 4.4.1 DEFINITION OF THE FISHER INFORMATION MATRIX 51 4.4.2 THE FISHER INFORMATION MATRIX FOR EXPONENTIAL FAMILIES OF DISTRIBUTIONS 55 4.4.3 INFLOW OF FISHER INFORMATION 56 4.5 LIMITS TO PRECISION: THE CRAMER-RAO LOWER BOUND 60 4.5.1 THE CRAMER-RAO LOWER BOUND FOR SCALAR FUNCTIONS OF SCALAR PARAMETERS 60 4.5.2 THE CRAMER-RAO LOWER BOUND FOR VECTOR FUNCTIONS OF VECTOR PARAMETERS 63 4.6 PROPERTIES OF THE CRAMER-RAO LOWER BOUND 66 4.6.1 INTERPRETATION OF THE EXPRESSION FOR THE CRAMER-RAO LOWER BOUND 66 4.6.2 THE CRAMER-RAO LOWER BOUND AS A MEASURE OF EFFICIENCY OF ESTIMATION 67 4.6.3 MONOTONICITY WITH THE NUMBER OF OBSERVATIONS 70 4.6.4 PROPAGATION OF STANDARD DEVIATION 70 4.6.5 INFLUENCE OF ESTIMATION OF ADDITIONAL PARAMETERS 71 4.6.6 THE CRAMER-RAO LOWER BOUND FOR BIASED ESTIMATORS 72 CONTENTS IX 4.7 THE CRAMER-RAO LOWER BOUND FOR COMPLEX PARAMETERS OR FUNCTIONS OF PARAMETERS 74 4.7.1 INTRODUCTION 74 4.7.2 THE CRAMER-RAO LOWER BOUND FOR VECTORS OF REAL AND COMPLEX FUNCTIONS OF REAL PARAMETERS 75 4.7.3 THE CRAMER-RAO LOWER BOUND FOR VECTORS OF REAL AND COMPLEX FUNCTIONS OF REAL AND COMPLEX PARAMETERS 76 4.8 THE CRAMER-RAO LOWER BOUND FOR EXPONENTIAL FAMILIES OF DISTRIBUTIONS 78 4.9 THE CRAMER-RAO LOWER BOUND AND IDENTINABILITY 79 4.10 THE CRAMER-RAO LOWER BOUND AND EXPERIMENTAL DESIGN 81 4.10.1 INTRODUCTION 81 4.10.2 EXPERIMENTAL DESIGN FOR NONLINEAR VECTOR PARAMETERS 84 4.11 COMMENTS AND REFERENCES 91 4.12 PROBLEMS 91 5 PRECISE AND ACCURATE ESTIMATION 99 5.1 INTRODUCTION 99 5.2 MAXIMUM LIKELIHOOD ESTIMATION 100 5.3 PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS 105 5.3.1 THE INVARIANCE PROPERTY OF MAXIMUM LIKELIHOOD ESTIMATORS 105 5.3.2 CONNECTION OF EFFICIENT UNBIASED ESTIMATORS AND MAXIMUM LIKELIHOOD ESTIMATORS 106 5.3.3 CONSISTENCY OF MAXIMUM LIKELIHOOD ESTIMATORS 106 5.3.4 ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS 110 5.3.5 ASYMPTOTIC EFFICIENCY OF MAXIMUM LIKELIHOOD ESTIMATORS 112 5.4 MAXIMUM LIKELIHOOD FOR NORMALLY DISTRIBUTED OBSERVATIONS 113 5.4.1 THE LIKELIHOOD FUNCTION FOR NORMALLY DISTRIBUTED OBSERVATIONS 113 5.4.2 PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS FOR NORMALLY DISTRIBUTED OBSERVATIONS 115 5.4.3 MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF LINEAR MODEIS FROM NORMALLY DISTRIBUTED OBSERVATIONS 121 5.5 MAXIMUM LIKELIHOOD FOR POISSON DISTRIBUTED OBSERVATIONS 123 5.6 MAXIMUM LIKELIHOOD FOR MULTINOMIALLY DISTRIBUTED OBSERVATIONS 124 5.7 MAXIMUM LIKELIHOOD FOR EXPONENTIAL FAMILY DISTRIBUTED OBSERVATIONS 125 5.8 TESTING THE EXPECTATION MODEL: THE LIKELIHOOD RATIO TEST 126 5.8.1 MODEL TESTING FOR ARBITRARY DISTRIBUTIONS 126 5.8.2 MODEL TESTING FOR EXPONENTIAL FAMILIES OF DISTRIBUTIONS 132 5.9 LEAST SQUARES ESTIMATION 134 5.10 NONLINEAR LEAST SQUARES ESTIMATION 136 5.11 LINEAR LEAST SQUARES ESTIMATION 139 5.12 WEIGHTED LINEAR LEAST SQUARES ESTIMATION 140 5.13 PROPERTIES OF THE LINEAR LEAST SQUARES ESTIMATOR 144 X CONTENTS 5.14 THE BEST LINEAR UNBIASED ESTIMATOR 145 5.15 SPECIAL CASES OF THE BEST LINEAR UNBIASED ESTIMATOR AND A RELATED RESULT 147 5.15.1 THE GAUSS-MARKOV THEOREM 147 5.15.2 NORMALLY DISTRIBUTED OBSERVATIONS 148 5.15.3 EXPONENTIAL FAMILY DISTRIBUTED OBSERVATIONS 148 5.16 COMPLEX LINEAR LEAST SQUARES ESTIMATION 149 5.17 SUMMARY OF PROPERTIES OF LINEAR LEAST SQUARES ESTIMATORS 151 5.18 RECURSIVE LINEAR LEAST SQUARES ESTIMATION 152 5.19 RECURSIVE LINEAR LEAST SQUARES ESTIMATION WITH FORGETTING 155 5.20 COMMENTS AND REFERENCES 157 5.21 PROBLEMS 158 NUMERICAL METHODS FOR PARAMETER ESTIMATION 163 6.1 INTRODUCTION 163 6.2 NUMERICAL OPTIMIZATION 164 6.2.1 KEY NOTIONS IN NUMERICAL OPTIMIZATION 164 6.2.2 REFERENCE LOG-LIKELIHOOD FUNCTIONS AND LEAST SQUARES CRITERIA 166 6.3 THE STEEPEST DESCENT METHOD 168 6.3.1 DEFINITION OF THE STEEPEST DESCENT STEP 168 6.3.2 PROPERTIES OF THE STEEPEST DESCENT STEP 171 6.4 THE NEWTON METHOD 174 6.4.1 DEFINITION OF THE NEWTON STEP 174 6.4.2 PROPERTIES OF THE NEWTON STEP 175 6.4.3 THE NEWTON STEP FOR MAXIMIZING LOG-LIKELIHOOD FUNCTIONS 182 6.5 THE FISHER SCORING METHOD 183 6.5.1 DEFINITION OF THE FISHER SCORING STEP 183 6.5.2 PROPERTIES OF THE FISHER SCORING STEP 183 6.5.3 FISHER SCORING STEP FOR EXPONENTIAL FAMILIES 185 6.6 THE NEWTON METHOD FOR NORMAL MAXIMUM LIKELIHOOD AND FOR NONLINEAR LEAST SQUARES 185 6.6.1 THE NEWTON STEP FOR NORMAL MAXIMUM LIKELIHOOD 185 6.6.2 THE NEWTON STEP FOR NONLINEAR LEAST SQUARES 187 6.7 THE GAUSS-NEWTON METHOD 188 6.7.1 DEFINITION OF THE GAUSS-NEWTON STEP 188 6.7.2 PROPERTIES OF THE GAUSS-NEWTON STEP 188 6.8 THE NEWTON METHOD FOR POISSON MAXIMUM LIKELIHOOD 191 6.9 THE NEWTON METHOD FOR MULTINOMIAL MAXIMUM LIKELIHOOD 192 6.10 THE NEWTON METHOD FOR EXPONENTIAL FAMILY MAXIMUM LIKELIHOOD 193 6.11 THE GENERALIZED GAUSS-NEWTON METHOD FOR EXPONENTIAL FAMILY MAXIMUM LIKELIHOOD 194 6.11.1 DEFINITION OF THE GENERALIZED GAUSS-NEWTON STEP 194 6.11.2 PROPERTIES OF THE GENERALIZED GAUSS-NEWTON METHOD 195 CONTENTS XI 6.12 THE ITERATIVELY REWEIGHTED LEAST SQUARES METHOD 197 6.13 THE LEVENBERG-MARQUARDT METHOD 197 6.13.1 DEFINITION OF THE LEVENBERG-MARQUARDT STEP 197 6.13.2 PROPERTIES OF THE LEVENBERG-MARQUARDT STEP 199 6.14 SUMMARY OF THE DESCRIBED NUMERICAL OPTIMIZATION METHODS 200 6.14.1 INTRODUCTION 200 6.14.2 THE STEEPEST ASCENT (DESCENT) METHOD 200 6.14.3 THE NEWTON METHOD 200 6.14.4 THE FISHER SCORING METHOD 201 6.14.5 THE GAUSS-NEWTON METHOD 201 6.14.6 THE GENERALIZED GAUSS-NEWTON METHOD 202 6.14.7 THE ITERATIVELY REWEIGHTED LEAST SQUARES METHOD 202 6.14.8 THE LEVENBERG-MARQUARDT METHOD 202 6.14.9 CONCLUSIONS 202 6.15 PARAMETER ESTIMATION METHODOLOGY 203 6.15.1 INTRODUCTION 203 6.15.2 INVESTIGATING THE FEASIBILITY OF THE OBSERVATIONS 203 6.15.3 PRELIMINARY SIMULATION EXPERIMENTS 204 6.16 COMMENTS AND REFERENCES 206 6.17 PROBLEMS 206 7 SOLUTIONS OR PARTIAL SOLUTIONS TO PROBLEMS 211 APPENDIX A: STATISTICAL RESULTS 247 A. 1 STATISTICAL PROPERTIES OF LINEAR COMBINATIONS OF STOCHASTIC VARIABLES 247 A.2 THE CAUCHY-SCHWARZ INEQUALITY FOR EXPECTATIONS 249 APPENDIX B: VECTORS AND MATRICES 251 B.L VECTORS 251 B.2 MATRICES 252 APPENDIX C: POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES 259 C.L REAL POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES 259 C.2 COMPLEX POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES 263 APPENDIX D: VECTOR AND MATRIX DIFFERENTIATION 265 REFERENCES 269 TOPIC INDEX 271
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id	DE-604.BV035115863
illustrated	Illustrated
index_date	2024-07-02T22:19:34Z
indexdate	2024-07-09T21:22:40Z
institution	BVB
isbn	0470147814 9780470147818
language	English
lccn	2007019912
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016783603
oclc_num	85829252
open_access_boolean
owner	DE-703 DE-29T DE-634
owner_facet	DE-703 DE-29T DE-634
physical	XIV, 273 S. graph. Darst.
publishDate	2007
publishDateSearch	2007
publishDateSort	2007
publisher	Wiley-Interscience
record_format	marc
spelling	Bos, Adriaan van den Verfasser aut Parameter estimation for scientists and engineers Adriaan van den Bos Hoboken, NJ Wiley-Interscience 2007 XIV, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 269-270) and index Estimation d'un paramètre Estimation, Théorie de l' Ingénierie - Méthodes statistiques Statistique mathématique Ingenieurwissenschaften Engineering Statistical methods Parameter estimation Parameteridentifikation (DE-588)4210689-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Parameter Mathematik (DE-588)4293830-2 gnd rswk-swf Parameter Mathematik (DE-588)4293830-2 s Parameteridentifikation (DE-588)4210689-8 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 http://www.loc.gov/catdir/toc/ecip0718/2007019912.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0739/2007019912-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0739/2007019912-b.html Contributor biographical information GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783603&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bos, Adriaan van den Parameter estimation for scientists and engineers Estimation d'un paramètre Estimation, Théorie de l' Ingénierie - Méthodes statistiques Statistique mathématique Ingenieurwissenschaften Engineering Statistical methods Parameter estimation Parameteridentifikation (DE-588)4210689-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Parameter Mathematik (DE-588)4293830-2 gnd
subject_GND	(DE-588)4210689-8 (DE-588)4128130-5 (DE-588)4293830-2
title	Parameter estimation for scientists and engineers
title_auth	Parameter estimation for scientists and engineers
title_exact_search	Parameter estimation for scientists and engineers
title_exact_search_txtP	Parameter estimation for scientists and engineers
title_full	Parameter estimation for scientists and engineers Adriaan van den Bos
title_fullStr	Parameter estimation for scientists and engineers Adriaan van den Bos
title_full_unstemmed	Parameter estimation for scientists and engineers Adriaan van den Bos
title_short	Parameter estimation for scientists and engineers
title_sort	parameter estimation for scientists and engineers
topic	Estimation d'un paramètre Estimation, Théorie de l' Ingénierie - Méthodes statistiques Statistique mathématique Ingenieurwissenschaften Engineering Statistical methods Parameter estimation Parameteridentifikation (DE-588)4210689-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Parameter Mathematik (DE-588)4293830-2 gnd
topic_facet	Estimation d'un paramètre Estimation, Théorie de l' Ingénierie - Méthodes statistiques Statistique mathématique Ingenieurwissenschaften Engineering Statistical methods Parameter estimation Parameteridentifikation Numerisches Verfahren Parameter Mathematik
url	http://www.loc.gov/catdir/toc/ecip0718/2007019912.html http://www.loc.gov/catdir/enhancements/fy0739/2007019912-d.html http://www.loc.gov/catdir/enhancements/fy0739/2007019912-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783603&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bosadriaanvanden parameterestimationforscientistsandengineers

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