Karlin / Amemiya / Goodman Studies in Econometrics, Time Series, and Multivariate Statistics

1. Auflage 2014
ISBN: 978-1-4832-6803-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 590 Seiten, Web PDF

Studies in Econometrics, Time Series, and Multivariate Statistics covers the theoretical and practical aspects of econometrics, social sciences, time series, and multivariate statistics. This book is organized into three parts encompassing 28 chapters. Part I contains studies on logit model, normal discriminant analysis, maximum likelihood estimation, abnormal selection bias, and regression analysis with a categorized explanatory variable. This part also deals with prediction-based tests for misspecification in nonlinear simultaneous systems and the identification in models with autoregressive errors. Part II highlights studies in time series, including time series analysis of error-correction models, time series model identification, linear random fields, segmentation of time series, and some basic asymptotic theory for linear processes in time series analysis. Part III contains papers on optimality properties in discrete multivariate analysis, Anderson's probability inequality, and asymptotic distributions of test statistics. This part also presents the comparison of measures, multivariate majorization, and of experiments for some multivariate normal situations. Studies on Bayes procedures for combining independent F tests and the limit theorems on high dimensional spheres and Stiefel manifolds are included. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

Autoren/Hrsg.

Karlin, Samuel

Amemiya, Takeshi

Goodman, Leo A.

Inhaltsverzeichnis

1;Front Cover;1
2;Studies in Econometrics, Time Series, and Multivariate Statistics;4
3;Copyright Page;5
4;Table of Contents;6
5;Contributors;10
6;Biographical Note;14
7;Bibliography of Theodore W. Anderson;16
8;PART I. Studies in Econometric and Quantitative Social Sciences;22
8.1;CHAPTER 1. A COMPARISON OF THE LOGIT MODEL AND NORMAL DISCRIMINANT ANALYSIS WHEN THE INDEPENDENT VARIABLES ARE BINARY;24
8.1.1;I. INTRODUCTION;24
8.1.2;II. BASIC FACTS;25
8.1.3;III. PREVIOUS RESULTS;28
8.1.4;IV. CASE OF ONE INDEPENDENT VARIABLE;31
8.1.5;V. CASE OF TWO INDEPENDENT VARIABLES;39
8.1.6;VI. SUMMARY AND CONCLUSIONS;47
8.1.7;APPENDIX;49
8.1.8;REFERENCES;51
8.2;CHAPTER 2. MAXIMUM LIKELIHOOD ESTIMATION IN A LATENT VARIABLE PROBLEM;52
8.2.1;I. INTRODUCTION;52
8.2.2;II. THE PARTICULAR PROBLEM;58
8.2.3;III. A GENERAL APPROACH;63
8.2.4;IV. SOME DETAILS;69
8.2.5;V. RESULTS;71
8.2.6;VI. DISCUSSION AND CONCLUDING REMARKS;77
8.2.7;ACKNOWLEDGMENTS;79
8.2.8;APPENDIX I;80
8.2.9;APPENDIX II. SOME DETAILS OF THE COMPUTATIONS;81
8.2.10;APPENDIX III;82
8.2.11;REFERENCES;85
8.3;CHAPTER 3. ABNORMAL SELECTION BIAS;88
8.3.1;I. INTRODUCTION;88
8.3.2;II. SPECIFICATION;90
8.3.3;III. TRUNCATED MEAN FUNCTIONS;91
8.3.4;IV. ANALYSIS;92
8.3.5;V. EXTENSIONS;97
8.3.6;VI. CONCLUSIONS;100
8.3.7;VII. APPENDIX A. LOGCONCAVITY AND THE TRUNCATED MEAN FUNCTION;101
8.3.8;VIII. APPENDIX B. LOGCONCAVITY FOR SPECIFIC DISTRIBUTIONS;103
8.3.9;ACKNOWLEDGMENTS;105
8.3.10;REFERENCES;105
8.4;CHAPTER 4. A NOTE ON A SUPPOSED CRITICISM OF AN ANDERSON-GOODMAN TEST IN MARKOV CHAIN ANALYSIS;106
8.4.1;I. INTRODUCTION;106
8.4.2;II. SOME EXAMPLES;107
8.4.3;III. THE UNMODIFIED AND MODIFIED TESTS;109
8.4.4;REFERENCES;113
8.5;CHAPTER 5. REGRESSION ANALYSIS WITH A CATEGORIZED EXPLANATORY VARIABLE;114
8.5.1;I. INTRODUCTION;114
8.5.2;II. THE MODEL;115
8.5.3;III. REGRESSION ON DUMMY VARIABLES;117
8.5.4;IV. REGRESSION O N MID-POINTS;121
8.5.5;V. MAXIMUM LIKELIHOOD ESTIMATION;124
8.5.6;VI. TWO STAGE ESTIMATION METHOD;132
8.5.7;VII. SOME GENERALIZATIONS;137
8.5.8;VIII. CONCLUSIONS;145
8.5.9;APPENDIX;145
8.5.10;ACKNOWLEDGMENTS;150
8.5.11;REFERENCES;150
8.6;CHAPTER 6. PREDICTION-BASED TESTS FOR MISSPECIFICATION IN NONLINEAR SIMULTANEOUS SYSTEMS;152
8.6.1;I. INTRODUCTION;152
8.6.2;II. BASIC CONCEPTS, PREDICTORS AND ASYMPTOTIC EXPANSIONS;155
8.6.3;III. TESTS OF MEAN PREDICTION ERROR;159
8.6.4;IV. REGRESSION TESTS;162
8.6.5;V. REGRESSION TESTS FOR LINEAR MODELS;164
8.6.6;VI. A NONLINEAR EXAMPLE;167
8.6.7;APPENDIX;171
8.6.8;REFERENCES;172
8.7;CHAPTER 7. ASYMPTOTIC PROPERTIES OF SOME ESTIMATORS IN STRUCTURAL MODELS;174
8.7.1;I. INTRODUCTION;174
8.7.2;II. THE MODEL AND ESTIMATORS;177
8.7.3;III. MAIN RESULTS;180
8.7.4;IV. STOCHASTIC EXPANSIONS AND APPROXIMATE CUMULANTS;182
8.7.5;V. CONCLUSIONS;187
8.7.6;REFERENCES;189
8.8;CHAPTER 8. IDENTIFICATION IN MODELS WITH AUTOREGRESSIVE ERRORS;190
8.8.1;I. INTRODUCTION;190
8.8.2;II. ALGEBRAIC PREREQUISITES;194
8.8.3;III. MULTIPLE SOLUTIONS;203
8.8.4;IV. FAILURE OF THE RANK CONDITIONS ON THE FIRST DERIVATIVE MATRIX;212
8.8.5;V. LOCAL UNIDENTIFIABILITY;214
8.8.6;VI. SOME SPECIAL CASES AND PRIOR PROBABILITIES;220
8.8.7;VII. ZERO ROOTS AND IDENTIFICATION;223
8.8.8;VIII. ALTERNATIVE APPROACHES AND GENERAL CONCLUSION;225
8.8.9;REFERENCES;225
8.9;CHAPTER 9. OPTIMAL STABILIZATION RULES IN A STOCHASTIC MODEL OF INVESTMENT WITH GESTATION LAGS;228
8.9.1;I. INTRODUCTION;228
8.9.2;II. AN INVESTMENT MODEL WITH HETEROGENEOUS GESTATION LAGS4;230
8.9.3;III. OPTIMAL POLICY RULES;233
8.9.4;IV. PROPERTIES OF OPTIMAL POLICY IN A SECOND ORDER CYCLICAL MODEL;240
8.9.5;V. STOCHASTIC SIMULATION RESULTS WITH SUBOPTIMAL POLICIES;241
8.9.6;VI. CONCLUDING REMARKS;245
8.9.7;ACKNOWLEDGMENTS;246
8.9.8;REFERENCES;247
8.10;CHAPTER 11. CANONICAL REPRESENTATION OF LINEAR STRUCTURAL ECONOMETRIC MODELS, RANK TESTS FOR IDENTIFICATION AND EXISTENCE OF ESTIMATORS' MOMENTS;248
8.10.1;I. INTRODUCTION;248
8.10.2;II. CANONICAL REPRESENTATIONS OF LINEAR STRUCTURAL ECONOMETRIC MODELS;249
8.10.3;III. TESTS FOR IDENTIFICATION AND EXISTENCE OF ESTIMATORS' MOMENTS;255
8.10.4;REFERENCES;261
9;PART II: Studies in Time Series;262
9.1;CHAPTER 11. THE PRICE OF IGNORANCE OF THE AUTOCORRELATION STRUCTURE OF THE ERRORS OF A REGRESSION MODEL;264
9.1.1;I. INTRODUCTION;264
9.1.2;II. SECOND ORDER APPROXIMATIONS TO SIGNIFICANCE POINTS FORTESTS ON REGRESSION COEFFICIENTS WHEN AUTOCORRELATION IN THE ERRORS HAS BEEN ALLOWED FOR;266
9.1.3;III. ADDITIONAL NUMBER OF OBSERVATIONS NEEDED DUE TO ESTIMATIONOF THE AUTOCORRELATION STRUCTURE;270
9.1.4;REFERENCES;274
9.2;CHAPTER 12. TIME SERIES ANALYSIS OF ERROR-CORRECTION MODELS;276
9.2.1;I. INTRODUCTION;276
9.2.2;II. THE ONE-WAY CAUSAL MODEL;278
9.2.3;III. MULTI-COMPONENT CO-INTEGRATED SERIES;281
9.2.4;IV. THE BIVARIATE FEEDBACK CASE;283
9.2.5;V. AGGREGATION;285
9.2.6;VI. TESTING FOR CO-INTEGRATION;286
9.2.7;VII. APPLICATION 1: EMPLOYEES' INCOME AND NATIONAL INCOME;290
9.2.8;VIII. APPLICATION 2. M3 AND GNP;292
9.2.9;IX. APPLICATION 3. PRICES, WAGES AND PRODUCTIVITY IN THE TRANSPORTATION INDUSTRY;294
9.2.10;X. CONCLUSIONS;296
9.2.11;APPENDIX 1. FRACTIONAL INTEGRATED SERIES;297
9.2.12;APPENDIX 2. ERROR CORRECTION AND SEASONALITY;298
9.2.13;REFERENCES;299
9.3;CHAPTER 13. TIME SERIES MODEL IDENTIFICATION BY ESTIMATING INFORMATION;300
9.3.1;I. INTRODUCTION;300
9.3.2;II. ROLE OF INFORMATION MEASURES IN MODEL IDENTIFICATION;301
9.3.3;III. INFORMATION FORMULATION OF TESTS FOR WHITE NOISE;307
9.3.4;IV. INFORMATION FORMULATION OF ARMA MODELS;309
9.3.5;V. MULTIPLE TIME SERIES MODEL IDENTIFICATION;312
9.3.6;VI. INFORMATION SUMMARY AND EXAMPLE;317
9.3.7;ACKNOWLEDGMENTS;319
9.3.8;REFERENCES;319
9.4;CHAPTER 14. LINEAR RANDOM FIELDS;320
9.4.1;I. INTRODUCTION;320
9.4.2;II. ARMA PROCESSES AND ARMA FIELDS;323
9.4.3;III. NON-GAUSSIAN LINEAR RANDOM FIELDS;328
9.4.4;REFERENCES;330
9.5;CHAPTER 15. ON SEGMENTATION OF TIME SERIES;332
9.5.1;I. INTRODUCTION;332
9.5.2;II. THE MODEL;333
9.5.3;III. AN ALGORITHM;338
9.5.4;IV. AN EXAMPLE;341
9.5.5;V. EXTENSIONS;350
9.5.6;REFERENCES;350
9.6;CHAPTER 16. PROPERTIES OF ESTIMATES OF THE MEAN SQUARE ERROR OF PREDICTION IN AUTOREGRESSIVE MODELS;352
9.6.1;I. INTRODUCTION;352
9.6.2;II. PRELIMINARIES;353
9.6.3;III. YULE-WALKER ESTIMATION;357
9.6.4;IV. LEAST SQUARES ESTIMATION;360
9.6.5;V. CONCLUDING REMARKS;361
9.6.6;REFERENCES;363
9.7;CHAPTER 17. A REEXAMINATION OF SOME BASIC ASYMPTOTIC THEORY FOR LINEAR PROCESSES IN TIME SERIES ANALYSIS;364
9.7.1;I. INTRODUCTION;364
9.7.2;II. AIMS OF THE PRESENT STUDY;366
9.7.3;III. STATEMENT OF ASSUMPTIONS AND METHODS OF ESTIMATION;367
9.7.4;IV. CONSISTENCY OF ESTIMATORS;373
9.7.5;V. ASYMPTOTIC NORMALITY OF ESTIMATES;388
9.7.6;VI. CONCLUDING REMARKS;395
9.7.7;APPENDIX;396
9.7.8;REFERENCES;396
10;PART III: Studies in Multivariate Statistics;398
10.1;CHAPTER 18. HYPOTHESIS TESTS AND OPTIMALITY PROPERTIES IN DISCRETE MULTIVARIATE ANALYSIS;400
10.1.1;I. INTRODUCTION AND SUMMARY;400
10.1.2;II. ADMISSIBILITY OF TESTS FOR POISSON SAMPLING;403
10.1.3;III. OPTIMALITY OF LRT FOR SOME HYPOTHESES DETERMINED BY LINEAR INEQUALITIES;406
10.1.4;IV. TESTING FOR COLLAPSIBILITY;416
10.1.5;V. TESTING EQUALITY OF PROPORTIONS;424
10.1.6;REFERENCES;426
10.2;CHAPTER 19. ON ANDERSON'S PROBABILITY INEQUALITY;428
10.2.1;I. INTRODUCTION;428
10.2.2;II. GENERALIZATIONS WITH SYMMETRIC FUNCTIONS;429
10.2.3;III. QUESTIONS ON MARGINAL FUNCTIONS;432
10.2.4;IV. RESULTS ON LOG-CONCAVE FUNCTIONS;433
10.2.5;V. MORE GENERAL INVARIANCE AND PRE-ORDERING;434
10.2.6;VI. ORDERING OF DISTRIBUTIONS;435
10.2.7;VII. RESULTS ON ASSOCIATION;436
10.2.8;REFERENCES;438
10.3;CHAPTER 20. ON ASYMPTOTIC DISTRIBUTIONS OF TEST STATISTICS FOR COVARIANCE MATRICES AND CORRELATION MATRICES;440
10.3.1;I. INTRODUCTION;440
10.3.2;II. ASYMPTOTIC DISTRIBUTIONS OF FUNCTIONS OF THE ELEMENTS OF SAMPLE COVARIANCE MATRIX;441
10.3.3;III. EFFECT OF OUTLIERS ON TESTS FOR CORRELATIONS;444
10.3.4;IV. ASYMPTOTIC JOINT DISTRIBUTIONS OF FUNCTIONS OF THE EIGENVALUES OF A MULTIVARIATE QUADRATIC FORM;447
10.3.5;V. SADDLE-POINT APPROXIMATIONS;451
10.3.6;VI. ROBUSTNESS OF TESTS ON EIGENVALUES OF COVARIANCE MATRICES;454
10.3.7;REFERENCES;455
10.4;CHAPTER 21. JOINT DISTRIBUTIONS OF SOME INDICES BASED ON CORRELATION COEFFICIENTS2;458
10.4.1;I. INTRODUCTION;458
10.4.2;II. SOME MOTIVATING EXAMPLES;461
10.4.3;III. A FUNDAMENTAL THEOREM;467
10.4.4;IV. JOINT DISTRIBUTIONS OF CORRELATION COEFFICIENTS;470
10.4.5;V. SPECIAL RESULTS FOR THE TRIVARIATE NORMAL DISTRIBUTION;473
10.4.6;REFERENCES;475
10.5;CHAPTER 22. ON THE WEDGE PRODUCT;476
10.5.1;I. INTRODUCTION;476
10.5.2;II. TRANSFORMATION OF THE DOUBLE INTEGRAL;477
10.5.3;III. DUAL;478
10.5.4;IV. TENSOR PRODUCT;479
10.5.5;V. SKEW SYMMETRIC WEDGE PRODUCT;480
10.5.6;VI. INVARIANT MEASURE ON THE ORTHOGONAL GROUP O(n) AND ITS COSET SPACES;482
10.5.7;REFERENCES;484
10.6;CHAPTER 23. COMPARISON OF MEASURES, MULTIVARIATE MAJORIZATION, AND APPLICATIONS TO STATISTICS;486
10.6.1;I. INTRODUCTION;486
10.6.2;II. DILATIONS;489
10.6.3;III. APPLICATIONS TO VARIOUS CONES OF FUNCTIONS ON RP;491
10.6.4;IV. CLASSES OF MULTIVARIATE SCHUR CONVEX FUNCTIONS;498
10.6.5;V. MULTIVARIATE SCHUR CONCAVITY AND LOG CONCAVITY;505
10.6.6;REFERENCES;510
10.7;CHAPTER 24. COMPARISON OF EXPERIMENTS FOR SOME MULTIVARIATE NORMAL SITUATIONS;512
10.7.1;SUMMARY;512
10.7.2;I. INTRODUCTION;512
10.7.3;II. TWO MULTIVARIATE NORMAL DISTRIBUTIONS;515
10.7.4;III. MULTIVARIATE NORMAL REGRESSION;517
10.7.5;IV. NONEXISTENCE OF CERTAIN UNBIASED ESTIMATORS;520
10.7.6;ACKNOWLEDGMENTS;524
10.7.7;REFERENCES;524
10.8;CHAPTER 25. BAYES PROCEDURES FOR COMBINING INDEPENDENT F TESTS;526
10.8.1;I. INTRODUCTION;526
10.8.2;II. CLASSES OF BAYES COMBINATION PROCEDURES;530
10.8.3;III. BAYES COMBINATION PROCEDURES SENSITIVE TO A PRESPECIFIED ALTERNATIVE;541
10.8.4;ACKNOWLEDGMENTS;548
10.8.5;REFERENCES;549
10.9;CHAPTER 26. LIKELIHOOD RATIO TESTS FOR RELATIONSHIPS BETWEEN TWO COVARIANCE MATRICES;550
10.9.1;I. INTRODUCTION;550
10.9.2;II. TEST FOR;552
10.9.3;III. TEST FOR ._2 = G + ó2 .;554
10.9.4;VI. FAMILIAL CORRELATIONS;560
10.9.5;ACKNOWLEDGMENTS;564
10.9.6;REFERENCES;564
10.10;CHAPTER 27. RANK ADDITIVITY AND MATRIX POLYNOMIALS;566
10.10.1;ACKNOWLEDGMENTS;579
10.10.2;REFERENCES;579
10.11;CHAPTER 28. LIMIT THEOREMS ON HIGH DIMENSIONAL SPHERES AND STIEFEL MANIFOLDS;580
10.11.1;I. INTRODUCTION;580
10.11.2;II. STIEFEL MANIFOLDS;582
10.11.3;III. NON-UNIFORM DISTRIBUTIONS ON Oq;586
10.11.4;REFERENCES;591