Statistical regression with measurement error:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Arnold
1999
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Kendall's library of statistics
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 262 S. graph. Darst. |
| ISBN: | 0340614617 |
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Datensatz im Suchindex
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| adam_text | IMAGE 1
STATISTICAL REGRESSION WITH
MEASUREMENT ERROR
CHI-LUN CHENG ACADEMIA SINICA, REPUBLIC OF CHINA
AND
JOHN W. VAN NESS UNIVERSITY OF TEXAS AT DALLAS
ARNOLD A MEMBER OF THE HODDER HEADLINE GROUP
LONDON * SYDNEY * AUCKLAND
CO-PUBLISHED IN THE USA BY OXFORD UNIVERSITY PRESS INC., NEW YORK
IMAGE 2
CONTENTS
PREFACE XIII
1 INTRODUCTION TO LINEAR MEASUREMENT ERROR MODELS 1
1.1 PRELIMINARIES 1
1.2 ELEMENTARY PROPERTIES OF MEASUREMENT ERROR MODELS 5
1.2.1 IDENTIFIABILITY OF THE MODEL 5
1.2.2 THE ROLE OF VARIABLES IN THE X KNOWN ME MODEL 9
1.2.3 ME REGRESSION WITH X KNOWN AND ORTHOGONAL REGRESSION 9
1.2.4 PREDICTION UNDER ME MODEIS 11
1.2.5 PRACTICAL MODEL BUILDING 12
1.3 MAXIMUM LIKELIHOOD ESTIMATION IN THE UNIVARIATE NORMAL MEASURE MENT
ERROR MODEL 13
1.3.1 MAXIMUM LIKELIHOOD ESTIMATION FOR THE STRUCTURAL RELATIONSHIP 14
1.3.2 MAXIMUM LIKELIHOOD ESTIMATION FOR THE FUNCTIONAL RELATIONSHIP 20
1.3.3 MAXIMUM LIKELIHOOD ESTIMATION FOR THE ULTRASTRUCTURAL RELA
TIONSHIP 26
1.4 THE ME MODEL WITH CORRELATED ERRORS 28
1.4.1 THE STRUCTURAL MODEL 28
1.4.2 THE FUNCTIONAL MODEL 30
1.5 THE EQUATION ERROR MODEL 31
1.5.1 THE STRUCTURAL EQUATION ERROR MODEL 32
1.5.2 THE FUNCTIONAL EQUATION ERROR MODEL 33
1.6 THE BERKSON MODEL 34
1.6.1 LEAST-SQAARES ESTIMATION FOR THE BERKSON MODEL 35
1.6.2 MAXIMUM LIKELIHOOD ESTIMATION FOR THE BERKSON MODEL 36 1.6.3 THE
BERKSON MODEL WITH EQUATION ERROR 38
1.6.4 FURTHER COMMENTS 39
1.7 MAXIMUM LIKELIHOOD ESTIMATION OF TRANSFORMED DATA: ELIMINATION OF
NUISANCE PARAMETERS 39
1.8 BIBLIOGRAPHIE NOTES AND DISCUSSION 41
IMAGE 3
VIII CONTENTS
1.8.1 ERROR IN THE EQUATION 42
1.8.2 MAXIMUM LIKELIHOOD ESTIMATION 43
1.8.3 THE BERKSON MODEL 44
1.8.4 TOTAL LEAST SQUARES 45
1.9 EXERCISES 45
PROPERTIES OF ESTIMATES AND PREDICTORS 49
2.1 ASYMPTOTIC PROPERTIES OF ME MODEL PARAMETER ESTIMATES 49
2.1.1 THE STRUCTURAL ME MODEL 49
2.1.2 THE FUNCTIONAL ME MODEL 50
2.1.3 THE ULTRASTRUCTURAL ME MODEL 52
2.2 ASYMPTOTIC PROPERTIES OF EQUATION ERROR MODEL ESTIMATES 56
2.3 FINITE-SAMPLE PROPERTIES 57
2.4 IMPLICATIONS REGARDING CONFIDENCE REGIONS 59
2.4.1 THE GLESER-HWANG EFFECT 60
2.4.2 ASYMPTOTIC CONFIDENCE REGIONS 60
2.4.3 CONFIDENCE SETS USING PIVOTAL STATISTICS: BOTH ERROR VARIANCES
KNOWN 62
2.4.4 CONFIDENCE SETS USING PIVOTAL STATISTICS: X, KNOWN 64
2.4.5 CONFIDENCE SETS FOR UNIDENTIFIABLE MODEIS 67
2.4.6 GENERAL COMMENTS 69
2.5 PREDICTION AND CALIBRATION UNDER MEASUREMENT ERROR MODELS 70
2.5.1 PREDICTION 70
2.5.2 CALIBRATION 72
2.6 BIBLIOGRAPHIE NOTES AND DISCUSSION 73
2.7 EXERCISES 74
2.8 RESEARCH PROBLEMS 75
COMPARING MODEL ASSUMPTIONS AND MODIFYING LEAST SQUARES 77 3.1 ISSUES
FACING USERS OF ME MODELS 77
3.2 A UNIFIED APPROACH TO THE FUNCTIONAL, STRUCTURAL, AND
ULTRASTRUCTURAL RELATIONSHIPS 78
3.3 IDENTIFIABILITY ASSUMPTIONS AND THE EQUATION ERROR MODEL 80
3.4 GENERALIZED LEAST SQUARES 82
3.5 MODIFIED LEAST SQUARES 84
3.5.1 DISCUSSION 86
3.6 BIBLIOGRAPHIE NOTES AND DISCUSSION 88
3.7 EXERCISES 89
ALTERNATIVE APPROACHES TO THE MEASUREMENT ERROR MODEL 93
4.1 INTRODUCTION AND OVERVIEW 93
4.2 INSTRUMENTAL VARIABLE ESTIMATORS 94
4.2.1 DEFINITION OF INSTRUMENTAL VARIABLES 94
4.2.2 MAXIMUM LIKELIHOOD ESTIMATION VIA INSTRUMENTAL VARIABLES 97 4.2.3
CONFIDENCE INTERVALS WITH INSTRUMENTAL VARIABLES 101
IMAGE 4
CONTENTS IX
4.3 GROUPING METHODS 103
4.3.1 TWO GROUPS 103
4.3.2 THREE GROUPS 112
4.4 METHODS BASED ON RANKS 118
4.4.1 CONFIDENCE INTERVALS FOR MEDIAN RANKING METHODS 120
4.5 METHODS OF HIGHER-ORDER MOMENTS AND PRODUCT CUMULANTS 120
4.5.1 GEARY S METHOD USING PRODUCT CUMULANTS 124
4.6 BIBLIOGRAPHIE NOTES AND DISCUSSION 129
4.7 EXERCISES 131
5 LINEAR MEASUREMENT ERROR MODEL WITH VECTOR EXPLANATORY VARIABLES 133
5.1 INTRODUCTION 133
5.2 IDENTIFIABILITY 134
5.3 THE EQUATION ERROR MODEL 134
5.3.1 MAXIMUM LIKELIHOOD ESTIMATION 134
5.3.2 THE RELIABILITY MATRIX KNOWN 137
5.4 MAXIMUM LIKELIHOOD FOR THE NO-EQUATION-ERROR MODEL 139
5.4.1 FUNCTIONAL MODEL WITH UNCORRELATED ERRORS 139
5.4.2 FUNCTIONAL AND STRUCTURAL MODEIS WITH CORRELATED ERRORS 143 5.5
ALTERNATIVE APPROACHES TO ESTIMATING THE PARAMETERS 144
5.5.1 INSTRUMENTAL VARIABLES 145
5.5.2 THE GENERALIZED AND MODIFIED LEAST-SQUARES ESTIMATORS 146 5.6
ASYMPTOTIC PROPERTIES OF THE ESTIMATES 147
5.7 BIBLIOGRAPHIE NOTES AND DISCUSSION 148
5.8 EXERCISES 149
5.9 RESEARCH PROBLEM 150
6 POLYNOMIAL MEASUREMENT ERROR MODELS 151
6.1 INTRODUCTION 151
6.1.1 CALCULATING THE FIT OF DATA TO A NONLINEAR ME MODEL 155
6.2 THE NONLINEAR STRUCTURAL MODEL 157
6.2.1 GLESER S CONDITIONAL APPROACH 157
6.2.2 THE CUMULANT METHOD 158
6.3 IDENTIFIABILITY IN NONLINEAR ME MODELS 164
6.4 POLYNOMIAL MODEL WITH EQUATION ERROR 165
6.4.1 THE CASE WHEN 8 AND E ARE INDEPENDENT 167
6.4.2 THE CASE WHEN 5 AND E ARE DEPENDENT 167
6.4.3 THE ADJUSTED LEAST-SQUARES ESTIMATOR UNDER NORMALITY 169
6.5 THE POLYNOMIAL FUNCTIONAL RELATIONSHIP WITHOUT EQUATION ERROR 171
6.5.1 A METHOD OF MOMENTS ESTIMATOR 171
6.5.2 EXTENDED GENERALIZED LEAST SQUARES 173
6.5.3 THE ERROR COVARIANCE MATRIX KNOWN UP TO A PROPORTIONALITY FACTOR
174
6.5.4 APPROXIMATION TO THE MAXIMUM LIKELIHOOD ESTIMATOR 174
L 6.5.5 AN ITERATIVE ALGORITHM 175
IMAGE 5
X CONTENTS
6.6 POLYNOMIAL BERKSON MODEL 177
6.7 BIBLIOGRAPHIE NOTES AND DISCUSSION 180
6.8 EXERCISES 183
7 ROBUST ESTIMATION IN MEASUREMENT ERROR MODELS 187
7.1 INTRODUCTION 187
7.1.1 THE INFLUENCE FUNETION 188
7.1.2 BREAKDOWN POINT 193
7.1.3 QUALITATIVE ROBUSTNESS 195
7.1.4 M-ESTIMATORS 196
7.2 ROBUST ORTHOGONAL REGRESSION 198
7.2.1 M-ESTIMATORS IN ORTHOGONAL REGRESSION 199
7.2.2 BOUNDED INFLUENCE ESTIMATORS AND HAMPEL S OPTIMALITY PROBLEM202
7.2.3 BIAS ROBUST ORTHOGONAL REGRESSION 207
7.3 ROBUST MEASUREMENT ERROR MODEL ESTIMATION VIA ROBUST COVARIANCE
MATRICES 210
7.4 COMPUTATIONAL METHODS FOR ROBUST ORTHOGONAL REGRESSION 212
7.4.1 THE ROREG ALGORITHM 214
7.4.2 MONTE CARLO STUDY OF ROREG 215
7.4.3 ROBUST CALIBRATION 219
7.5 BIBLIOGRAPHIE NOTES AND DISCUSSION 220
7.6 EXERCISES 222
7.7 RESEARCH PROBLEM 222
8 ADDITIONAL TOPICS 223
8.1 ESTIMATION OF THE TRUE VARIABLES 223
8.1.1 THE LINEAR STRUCTURAL MODEL WITHOUT EQUATION ERROR 223
8.1.2 THE LINEAR FUNCTIONAL MODEL WITHOUT EQUATION ERROR 224
8.1.3 THE EQUATION ERROR MODEL 225
8.1.4 THE NONLINEAR MODEL 225
8.2 OBTAINING IDENTIFIABILITY ASSUMPTION INFORMATION 226
8.2.1 EQUAL NUMBER OF REPLICATIONS WITH UNCORRELATED ERRORS 226 8.2.2
UNEQUAL NUMBER OF REPLICATIONS 227
8.2.3 CORRELATED MEASUREMENT ERRORS 228
8.2.4 VALIDATION DATA 228
8.3 CONCLUSIONS 229
8.4 RELATIONS TO OTHER LATENT VARIABLES MODELS 229
8.4.1 SIMULTANEOUS EQUATIONS ME MODEL 229
8.5 THE FACTOR ANALYSIS MODEL 230
8.5.1 OTHER LATENT VARIABLE MODEIS 231
8.6 TERMINOLOGY 231
8.7 EXERCISES 232
IMAGE 6
CONTENTS XI
APPENDIX A. IDENTIFICATION IN MEASUREMENT ERROR MODELS 235
A. 1 OVERVIEW 235
A.2 STRUCTURAL MODEL 235
A.3 FUNCTIONAL MODEL 238
A.4 IDENTIFIABILITY AND CONSISTENT ESTIMATION 239
BIBLIOGRAPHY 241
AUTHORINDEX 253
SUBJECT INDEX 257
|
| any_adam_object | 1 |
| author | Cheng, Chi-Lun Van Ness, John W. |
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| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| indexdate | 2024-07-09T18:25:45Z |
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| language | English |
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| physical | XIV, 262 S. graph. Darst. |
| publishDate | 1999 |
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| publishDateSort | 1999 |
| publisher | Arnold |
| record_format | marc |
| series | Kendall's library of statistics |
| series2 | Kendall's library of statistics |
| spelling | Cheng, Chi-Lun Verfasser aut Statistical regression with measurement error Chi-Lun Cheng and John W. Van Ness 1. publ. London [u.a.] Arnold 1999 XIV, 262 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kendall's library of statistics 6 Regression Analysis cabt Analyse de régression ram Foutenleer gtt Metingen gtt Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Messfehler (DE-588)4133270-2 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Messfehler (DE-588)4133270-2 s DE-604 Mathematisches Modell (DE-588)4114528-8 s DE-188 Van Ness, John W. Verfasser aut Kendall's library of statistics 6 (DE-604)BV010165867 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008363034&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cheng, Chi-Lun Van Ness, John W. Statistical regression with measurement error Kendall's library of statistics Regression Analysis cabt Analyse de régression ram Foutenleer gtt Metingen gtt Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Messfehler (DE-588)4133270-2 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4114528-8 (DE-588)4133270-2 |
| title | Statistical regression with measurement error |
| title_auth | Statistical regression with measurement error |
| title_exact_search | Statistical regression with measurement error |
| title_full | Statistical regression with measurement error Chi-Lun Cheng and John W. Van Ness |
| title_fullStr | Statistical regression with measurement error Chi-Lun Cheng and John W. Van Ness |
| title_full_unstemmed | Statistical regression with measurement error Chi-Lun Cheng and John W. Van Ness |
| title_short | Statistical regression with measurement error |
| title_sort | statistical regression with measurement error |
| topic | Regression Analysis cabt Analyse de régression ram Foutenleer gtt Metingen gtt Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Messfehler (DE-588)4133270-2 gnd |
| topic_facet | Regression Analysis Analyse de régression Foutenleer Metingen Regressieanalyse Regression analysis Regressionsanalyse Mathematisches Modell Messfehler |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008363034&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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