Exponential familiy nonlinear models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore ; Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Tokyo
Springer
1998
|
| Series: | Lecture notes in statistics
Vol. 130 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 211 - 222 |
| Physical Description: | IX, 230 S. graph. Darst. |
| ISBN: | 9813083298 |
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Record in the Search Index
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| adam_text | BO-CHENG WEI
EXPONENTIAL FAMILY
NONLINEAR MODELS
SPRINGER
CONTENTS
1 EXPONENTIAL FAMILY- 1
1.1 EXPONENTIAL FAMILY 1
1.2 LIKELIHOOD 7
1.3 LIKELIHOOD RATIO AND DEVIANCE 9
2 EXPONENTIAL FAMILY NONLINEAR MODELS 13
2.1 DEFINITION 13
2.2 LIKELIHOOD . . 19
2.3 COMPUTATION AND EXAMPLES 24
3 GEOMETRIC FRAMEWORK 29
3.1 INTRODUCTION 29
3 .2 GEOMETRY IN EXPECTATION PARAMETER SPACE 31
3.2.1 CURVATURE ARRAYS 32
3.2.2 DIRECTIONAL CURVATURES AND MAXIMUM CURVATURES ... 35
3.2.3 PARAMETER TRANSFORMATION 40
3.3 GEOMETRY IN NATURAL PARAMETER SPACE 44
3.4 SOME SPECIFIC MODELS 49
3.4.1 NORMAL NONLINEAR REGRESSION MODELS 49
3.4.2 GENERALIZED LINEAR MODELS 49
3.4.3 ONE-PARAMETER MODEL AND EFRON CURVATURE 51
4 SOME SECOND ORDER ASYMPTOTICS 55
4.1 STOCHASTIC EXPANSIONS 56
4.2 APPROXIMATE BIAS AND VARIANCE 64
4.3 INFORMATION LOSS 71
VLL
VIII CONTENTS
4.4 OBSERVED INFORMATION AND FISHER INFORMATION 76
5 CONFIDENCE REGIONS 83
5.1 INTRODUCTION 84
5.2 LIKELIHOOD REGION IN TERMS OF CURVATURES 86
5.2.1 TANGENT SPACE PROJECTION OF LIKELIHOOD REGION 86
5.2.2 INFLUENCE OF CURVATURE MEASURES 90
5.3 CONFIDENCE REGIONS FOR PARAMETER SUBSETS 93
5.3.1 REGION BASED ON LIKELIHOOD RATIO STATISTIC 94
5.3.2 REGION BASED ON SCORE STATISTIC 96
6 DIAGNOSTICS AND INFLUENCE ANALYSIS 101
6.1 INTRODUCTION 101
6.2 ANALYSIS OF DIAGNOSTIC MODELS 105
6.2.1 DIAGNOSTIC MODELS 105
6.2.2 REGRESSION COEFFICIENTS - 106
6.2.3 DEVIANCE AND DISPERSION PARAMETER : . . . . 109
6.2.4 SCORE STATISTIC OF OUTLIER 112
6.3 INFLUENCE DIAGNOSTICS BASED ON CASE DELETION 116
6.3.1 DIAGNOSTICS BASED ON WEIGHTED LEAST SQUARES 116
6.3.2 DIAGNOSTICS BASED ON DEVIANCE 119
6.4 LOCAL INFLUENCE ANALYSIS 123
6.4.1 PERTURBED MODELS 123
6.4.2 RANDOM PERTURBATION SCHEME 128
6.5 GENERALIZED LEVERAGE 136
6.5.1 DEFINITION AND COMPUTATION 136
6.5.2 GENERALIZED LEVERAGE AND LOCAL INFLUENCE 140
6.6 DIAGNOSTICS FOR VARYING DISPERSION 141
6.6.1 LIKELIHOOD RATIO AND SCORE STATISTICS 142
6.6.2 ADJUSTED LIKELIHOOD RATIO AND SCORE STATISTICS 147
6.6.3 EXAMPLES 155
6.6.4 SIMULATION STUDY .-.** 158
7 EXTENSION 165
7.1 CURVED EXPONENTIAL FAMILIES 166
7.1.1 INTRODUCTION AND GEOMETRIC FRAMEWORK . 166
CONTENTS IX
7.1.2 STATISTICAL ANALYSIS 167
7.2 MULTINOMIAL NONLINEAR MODELS . 170
7.3 EMBEDDED MODELS 174
7.4 QUASI-LIKELIHOOD MODELS 177
7.5 COVARIANCE STRUCTURE MODELS 179
APPENDIX 185
A MATRIX AND ARRAY 185
A.I PROJECTION IN WEIGHTED INNER PRODUCT SPACE 185
A.2 ARRAY MULTIPLICATION 188
A.3 DIFFERENTIATION OF VECTOR AND MATRIX 191
B SOME ASYMPTOTIC RESULTS 195
B.I NOTATION AND PREPARATION 195
B.2 NECESSARY CONDITION OF CONSISTENCY 196
B.3 CONSISTENCY AND ASYMPTOTIC NORMALITY 199
B.4 ASYMPTOTIC NUMERICAL STABILITY OF ITERATIONS 208
BIBLIOGRAPHY 211
AUTHOR INDEX 223
SUBJECT INDEX 227
|
| adam_txt |
BO-CHENG WEI
EXPONENTIAL FAMILY
NONLINEAR MODELS
SPRINGER
CONTENTS
1 EXPONENTIAL FAMILY- " 1
1.1 EXPONENTIAL FAMILY 1
1.2 LIKELIHOOD 7
1.3 LIKELIHOOD RATIO AND DEVIANCE 9
2 EXPONENTIAL FAMILY NONLINEAR MODELS 13
2.1 DEFINITION 13
2.2 LIKELIHOOD . . 19
2.3 COMPUTATION AND EXAMPLES 24
3 GEOMETRIC FRAMEWORK 29
3.1 INTRODUCTION 29
3'.2 GEOMETRY IN EXPECTATION PARAMETER SPACE 31
3.2.1 CURVATURE ARRAYS 32
3.2.2 DIRECTIONAL CURVATURES AND MAXIMUM CURVATURES . 35
3.2.3 PARAMETER TRANSFORMATION 40
3.3 GEOMETRY IN NATURAL PARAMETER SPACE 44
3.4 SOME SPECIFIC MODELS 49
3.4.1 NORMAL NONLINEAR REGRESSION MODELS 49
3.4.2 GENERALIZED LINEAR MODELS 49
3.4.3 ONE-PARAMETER MODEL AND EFRON CURVATURE 51
4 SOME SECOND ORDER ASYMPTOTICS 55
4.1 STOCHASTIC EXPANSIONS 56
4.2 APPROXIMATE BIAS AND VARIANCE 64
4.3 INFORMATION LOSS 71
VLL
VIII CONTENTS
4.4 OBSERVED INFORMATION AND FISHER INFORMATION 76
5 CONFIDENCE REGIONS 83
5.1 INTRODUCTION 84
5.2 LIKELIHOOD REGION IN TERMS OF CURVATURES 86
5.2.1 TANGENT SPACE PROJECTION OF LIKELIHOOD REGION 86
5.2.2 INFLUENCE OF CURVATURE MEASURES 90
5.3 CONFIDENCE REGIONS FOR PARAMETER SUBSETS 93
5.3.1 REGION BASED ON LIKELIHOOD RATIO STATISTIC 94
5.3.2 REGION BASED ON SCORE STATISTIC 96
6 DIAGNOSTICS AND INFLUENCE ANALYSIS 101
6.1 INTRODUCTION 101
6.2 ANALYSIS OF DIAGNOSTIC MODELS 105
6.2.1 DIAGNOSTIC MODELS 105
6.2.2 REGRESSION COEFFICIENTS - 106
6.2.3 DEVIANCE AND DISPERSION PARAMETER : . . . . 109
6.2.4 SCORE STATISTIC OF OUTLIER 112
6.3 INFLUENCE DIAGNOSTICS BASED ON CASE DELETION 116
6.3.1 DIAGNOSTICS BASED ON WEIGHTED LEAST SQUARES 116
6.3.2 DIAGNOSTICS BASED ON DEVIANCE 119
6.4 LOCAL INFLUENCE ANALYSIS 123
' 6.4.1 PERTURBED MODELS 123
6.4.2 RANDOM PERTURBATION SCHEME 128
6.5 GENERALIZED LEVERAGE ' 136
6.5.1 DEFINITION AND COMPUTATION 136
6.5.2 GENERALIZED LEVERAGE AND LOCAL INFLUENCE 140
6.6 DIAGNOSTICS FOR VARYING DISPERSION 141
6.6.1 LIKELIHOOD RATIO AND SCORE STATISTICS 142
6.6.2 ADJUSTED LIKELIHOOD RATIO AND SCORE STATISTICS 147
6.6.3 EXAMPLES 155
6.6.4 SIMULATION STUDY .-.**' 158
7 EXTENSION 165
7.1 CURVED EXPONENTIAL FAMILIES 166
7.1.1 INTRODUCTION AND GEOMETRIC FRAMEWORK . 166
CONTENTS IX
7.1.2 STATISTICAL ANALYSIS 167
7.2 MULTINOMIAL NONLINEAR MODELS .' 170
7.3 EMBEDDED MODELS 174
7.4 QUASI-LIKELIHOOD MODELS 177
7.5 COVARIANCE STRUCTURE MODELS 179
APPENDIX 185
A MATRIX AND ARRAY 185
A.I PROJECTION IN WEIGHTED INNER PRODUCT SPACE 185
A.2 ARRAY MULTIPLICATION 188
A.3 DIFFERENTIATION OF VECTOR AND MATRIX 191
B SOME ASYMPTOTIC RESULTS 195
B.I NOTATION AND PREPARATION 195
B.2 NECESSARY CONDITION OF CONSISTENCY 196
B.3 CONSISTENCY AND ASYMPTOTIC NORMALITY 199
B.4 ASYMPTOTIC NUMERICAL STABILITY OF ITERATIONS 208
BIBLIOGRAPHY 211
AUTHOR INDEX 223
SUBJECT INDEX 227 |
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| institution | BVB |
| isbn | 9813083298 |
| language | English |
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| physical | IX, 230 S. graph. Darst. |
| publishDate | 1998 |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Wei, Bo-Cheng Verfasser aut Exponential familiy nonlinear models Bo-Cheng Wei Singapore ; Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Tokyo Springer 1998 IX, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics Vol. 130 Literaturverz. S. 211 - 222 Exponential families (Statistics) Nonlinear theories Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd rswk-swf Exponentialfamilie (DE-588)4372302-0 gnd rswk-swf Exponentialfamilie (DE-588)4372302-0 s Nichtlineares Regressionsmodell (DE-588)4251078-8 s DE-604 Lecture notes in statistics Vol. 130 (DE-604)BV002447846 130 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016878576&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wei, Bo-Cheng Exponential familiy nonlinear models Lecture notes in statistics Exponential families (Statistics) Nonlinear theories Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd Exponentialfamilie (DE-588)4372302-0 gnd |
| subject_GND | (DE-588)4251078-8 (DE-588)4372302-0 |
| title | Exponential familiy nonlinear models |
| title_auth | Exponential familiy nonlinear models |
| title_exact_search | Exponential familiy nonlinear models |
| title_exact_search_txtP | Exponential familiy nonlinear models |
| title_full | Exponential familiy nonlinear models Bo-Cheng Wei |
| title_fullStr | Exponential familiy nonlinear models Bo-Cheng Wei |
| title_full_unstemmed | Exponential familiy nonlinear models Bo-Cheng Wei |
| title_short | Exponential familiy nonlinear models |
| title_sort | exponential familiy nonlinear models |
| topic | Exponential families (Statistics) Nonlinear theories Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd Exponentialfamilie (DE-588)4372302-0 gnd |
| topic_facet | Exponential families (Statistics) Nonlinear theories Nichtlineares Regressionsmodell Exponentialfamilie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016878576&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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