Improved methods of inference in econometrics:
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Amsterdam [u.a.]
North-Holland
1986
|
Schriftenreihe: | Studies in mathematical and managerial economics
34 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVI, 291 S. graph. Darst. |
ISBN: | 0444879366 |
Internformat
MARC
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Datensatz im Suchindex
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adam_text | IMPROVED METHODS
OF INFERENCE
IN ECONOMETRICS
GEORGE G JUDGE
UNIVERSITY OF ILLINOIS
UNIVERSITY OF CALIFORNIA , BERKELEY
and
THOMAS A YANCEY
UNIVERSITY OF ILLINOIS
NORTH-HOLLAND
AMSTERDAM • NEW YORK • OXFORD • TOKYO
CONTENTS
1 Introduction 1
1 1 Organization of the Book 3
1 2 References 4
Part I - The Inferential and Decision Framework
2 The Measure of Performance 7
2 1 The Information Space 7
2 2 The Classical Approach 7
2 3 The Decision Theory Approach 8
231 Choosing a decision rule 9
232 The measure space 11
2 4 References 13
3 Some Alternative Statistical Models, Estimators and Tests IS
3 1 The Classical Linear Statistical Model, Estimator and Test Statistic 15
3 2 Measures of Performance 17
3 3 Some Alternative Estimators 20
331 Exact non-sample information 20
332 Stochastic non-sample information 22
333 An informative proper prior distribution 24
3 4 Pre-Test Estimators 25
341 Conventional equality pre-test estimator 26
3 5 Conventional Estimator Inadmissibility and the Stein-Rule Alternatives 28
351 Estimation under squared error loss 29
352 Stein-like rules under weighted squared error loss 34
3 6 Estimation with Non-Normal Errors 37
3 7 Some Final Comments 38
3 8 References 39
Part II - Inequality Estimation and Hypothesis Testing
4 Inequality Estimation and Hypothesis Testing of the Location
Parameter of a Normal Random Variable 43
4 1 Introduction 43
xii Contents
4 2 The Inequality Estimator and Its Sampling Properties 43
421 The mean of g* 45
422 The risk of the inequality estimator 46
423 Variance of the inequality restricted estimator 49
424 Comment 51
425 Extensions 52
426 Summary remarks 55
4 3 Inequality Hypothesis Testing 56
431A hypothesis testing framework 56
432 Test statistic and pre-test estimator 57
433 Mean of the inequality pre-test estimator 58
434 Risk of the inequality pre-test estimator 60
435 Variance of the pre-test estimator 63
436 Hypothesis testing, a2 unknown 63
437 Concluding remarks 66
4 4 The Sampling Performance of Pre-Test Estimators of the Scale Parameter
Under Squared Error Loss 66
441 The statistical model and estimators 66
442 The pre-test estimator a2 67
443 The inequality pre-test estimator a 2 68
444 Minimum mean square pre-test estimator o2 70
445 Some final remarks 71
4 5 References 71
Appendix 4 A: A Theorem and Some Corollaries 72
Appendix 4 B: Derivative of the Bias of the Inequality Restricted Estimator g* 76
Appendix 4 C: Convergence Theorem 77
Appendix 4 D: Estimator Bias and Risk Values 78
5 General Linear Statistical Model and a Single Linear Inequality
Constraint 81
5 1 Introduction 81
5 2 The Statistical Model and Estimators 81
5 3 The Mean of the Inequality Restricted Estimator 85
5 4 The Risk Function of the Inequality Restricted Estimator 87
541 The measure space 87
542 The risk 88
5 5 Mean and Covariance of b* 91
5 6 Generalizations 93
5 7 Hypothesis Testing 94
571 Test statistic and pre-test estimator, a2 known 95
572 Pre-test mean 96
573 The risk 97
Contents xiii
5 8 Some Comments 98
5 9 References 99
6 Inequality Restricted Estimation of Two or More
Location Parameters: The Orthonormal Case 101
6 1 The Inequality Restricted Estimator with Two Restrictions 101
611 The mean and bias of the IRMLE 103
612 The risk function of the inequality restricted estimator 106
613 The variance-covariance matrix 109
6 2 The IRMLE with Three Restrictions 109
621 The mean and bias 112
622 The risk function and variances 113
6 3 The IRMLE with K Restrictions 114
631 The risk function 115
632 The variance-covariance matrix 116
6 4 Summary and Conclusions 117
6 5 References 117
7 An Inequality Restricted Stein Rule Estimator 119
7 1 Statistical Model and Estimators 119
7 2 The Inequality Prior Information Estimator and Its Risk 120
7 3 An Inequality Restricted Stein Estimator (IRSE) 122
731 The estimator 122
732 Risk of the Stein inequality estimator 123
7 4 Estimator Risk Comparisons 125
7 5 Risk Evaluations 127
7 6 Bias, Variance and Component Risks 129
7 7 Positive Part Stein Estimation, Restricted and Unrestricted 131
7 8 Summary and Conclusions 133
7 9 References 134
Appendix 134
8 Hypothesis Testing for Two or More Inequalities:
The Orthogonal Case 137
8 1 Hypothesis Testing with Equality Constraints 138
8 2 Hypothesis Testing with Two or More Inequality Constraints 139
821 Hypothesis testing with two inequality constraints 139
822A likelihood ratio test: Known variance case, H0: 9 0 142
823A likelihood ratio test: Variance unknown, H0: 0=0 144
824 Hypothesis testing with three inequality constraints:
Known variance case 145
825 Hypothesis testing with K inequality constraints 149
x;v Contents
826 Illustrative c2 values for alternative a levels and numbers of
inequalities 151
8 3 Power Function Comparisons: Two Inequality Hypotheses 152
831 The known variance case 152
832 The unknown variance case 157
8 4 Hypothesis Testing with an Unknown Variance 158
841 The two inequality hypothesis case 159
842 Hypothesis testing with K constraints 164
8 5 Mixed Inequality and Equality Hypotheses 165
851 The one equality and one inequality hypothesis case:
Variance known 165
852J inequalities and ( H — J ) equality hypotheses 166
8 6 One-Sided Confidence Regions 171
8 7 Summary and Conclusions 173
8 8 References 174
Appendix 174
9 Inequality Restricted Estimation: General Design and
Restriction Matrices 179
9 1 The General Inequality Restricted Estimator 179
911 Kuhn-Tucker conditions and a primal-dual formulation 180
912 Expressions for the inequality restricted estimator 183
9 2 The Reparameterized Model 186
921 The inequality restricted estimator 189
9 3 The Mean of the Inequality Restricted Estimator 191
9 4 The Risk Function of the Inequality Restricted Estimator 193
941 Measure space 193
942 The risk 193
9 5 Risk Matrix for ft* 199
9 6 Mean and Covariance of ft* 204
9 7 Summary 205
9 8 References 205
10 Inequality Hypothesis Testing: General Case 207
10 1 Introduction 207
10 2 Inequality Hypothesis Testing: General R and X for Two Parameters 207
10 2 1 Hypothesis testing in non-orthogonal cases 208
10 2 2 Testing general linear inequality hypotheses 210
10 3 Hypothesis Testing for the Linear Model in the General X and R Case 216
10 4 Inequality Hypothesis Testing: Unknown Variance 218
10 4 1 H0: A9 = 0 and H„: A8 £ 0 219
10 4 2 H0: Ati0 and H,: 222
Contents xv
10 5 Confidence Regions with General X in Two or More Dimensions 225
10 6 Summary and Conclusions 228
10 7 References 229
Appendix 230
Part III - Some Sampling Results for the Stein Family
of Estimators
11 Assessing the Precision of Stein s Estimator 239
11 1 The Statistical Model and Estimators 239
11 2 The Empirical Bayes Estimator 240
11 2 1 Stein empirical Bayes confidence interval 241
11 3 The Bootstrap Approach 243
11 4 The Sampling Experiment Results 243
11 5: Summary and Implications 245
11 6 References 246
12 Some Evaluations of the Sampling Performance of the
Limited Translation and New Stein Estimators 247
12 1 Introduction 247
12 2 The Limited Translation Estimator 248
12 2 1 Sampling characteristics of the limited translation estimator 249
12 2 2 Conclusions 250
12 3 The New Stein Estimator 251
12 3 1 Sampling characteristics of the new Stein estimator 254
12 4 The Use of the New Stein /* as a Criterion in Model Selection 255
12 41A Monte Carlo sampling experiment 256
12 5 References 258
13 Estimation Under Non-Normal Errors and Quadratic Loss 259
13 1 Introduction 259
13 2 The Statistical Model and Estimators 260
13 2 1 Maximum likelihood estimators 260
13 2 2 The L estimators 261
13 2 3 James and Stein estimators 262
13 2 4 New Stein estimators 263
13 3 The Sampling Experiment 265
13 3 1 Independent univariate Student-/ 265
13 3 2 Multivariate Student-/ 266
13 3 3 The new Stein estimator 267
13 3 4 Component risks 269
xvi Contents
13 4 Concluding Remarks 271
13 5 References _ 271
14 Estimation and Hypothesis Testing in the Case of Possible
Heteroskedasticity 273
14 1 Statistical Model and Traditional Estimators 273
14 2 Improved Estimators 275
14 2 1 Known scale parameters (least squares format) 276
14 2 2 Known scale parameters (Aitken format) 277
14 2 3 Unknown scale parameters (least squares format) 278
14 2 4 Unknown scale parameters (Aitken format) 281
14 3 Empirical Risk Functions 283
14 4 Non-Optimality of the Traditional Pre-Test Estimator 285
14 5 Summary 287
14 6 References 288
Subject Index 289
|
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author | Judge, George G. 1925- Yancey, Thomas Alexander |
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dewey-tens | 330 - Economics |
discipline | Mathematik Wirtschaftswissenschaften |
format | Book |
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institution | BVB |
isbn | 0444879366 |
language | English |
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spelling | Judge, George G. 1925- Verfasser (DE-588)12963221X aut Improved methods of inference in econometrics George G. Judge and Thomas A. Yancey Amsterdam [u.a.] North-Holland 1986 XVI, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in mathematical and managerial economics 34 Décision, prise de ram Econométrie ram Prise de décision Tests d'hypothèses (Statistique) Tests d'hypothèses (Statistique) ram Économétrie Econometrics Decision making Statistical hypothesis testing Ökonometrie (DE-588)4132280-0 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Entscheidungsprozess (DE-588)4121202-2 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 s Ökonometrie (DE-588)4132280-0 s DE-604 Entscheidungsprozess (DE-588)4121202-2 s Statistischer Test (DE-588)4077852-6 s Yancey, Thomas Alexander Verfasser (DE-588)170050602 aut Studies in mathematical and managerial economics 34 (DE-604)BV001887014 34 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002359789&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Judge, George G. 1925- Yancey, Thomas Alexander Improved methods of inference in econometrics Studies in mathematical and managerial economics Décision, prise de ram Econométrie ram Prise de décision Tests d'hypothèses (Statistique) Tests d'hypothèses (Statistique) ram Économétrie Econometrics Decision making Statistical hypothesis testing Ökonometrie (DE-588)4132280-0 gnd Inferenzstatistik (DE-588)4247120-5 gnd Entscheidungsprozess (DE-588)4121202-2 gnd Statistischer Test (DE-588)4077852-6 gnd |
subject_GND | (DE-588)4132280-0 (DE-588)4247120-5 (DE-588)4121202-2 (DE-588)4077852-6 |
title | Improved methods of inference in econometrics |
title_auth | Improved methods of inference in econometrics |
title_exact_search | Improved methods of inference in econometrics |
title_full | Improved methods of inference in econometrics George G. Judge and Thomas A. Yancey |
title_fullStr | Improved methods of inference in econometrics George G. Judge and Thomas A. Yancey |
title_full_unstemmed | Improved methods of inference in econometrics George G. Judge and Thomas A. Yancey |
title_short | Improved methods of inference in econometrics |
title_sort | improved methods of inference in econometrics |
topic | Décision, prise de ram Econométrie ram Prise de décision Tests d'hypothèses (Statistique) Tests d'hypothèses (Statistique) ram Économétrie Econometrics Decision making Statistical hypothesis testing Ökonometrie (DE-588)4132280-0 gnd Inferenzstatistik (DE-588)4247120-5 gnd Entscheidungsprozess (DE-588)4121202-2 gnd Statistischer Test (DE-588)4077852-6 gnd |
topic_facet | Décision, prise de Econométrie Prise de décision Tests d'hypothèses (Statistique) Économétrie Econometrics Decision making Statistical hypothesis testing Ökonometrie Inferenzstatistik Entscheidungsprozess Statistischer Test |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002359789&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV001887014 |
work_keys_str_mv | AT judgegeorgeg improvedmethodsofinferenceineconometrics AT yanceythomasalexander improvedmethodsofinferenceineconometrics |