A primer in econometric theory

This book offers a cogent and concise treatment of econometric theory and methods along with the underlying ideas from statistics, probability theory, and linear algebra. It emphasizes foundations and general principles, but also features many solved exercises, worked examples, and code listings. Af... Ausführliche Beschreibung

1. Person: Stachurski, John
Format: Buch
Sprache: English
Veröffentlicht: Cambridge, MA [u.a.] MIT Press 2016
Beschreibung: XVII, 430 S. graph. Darst.
Schlagworte (STW): Ökonometrie
Theorie
Schlagworte (SH): Economics
Statistical methods
Mathematical models
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245 0 2 |a A primer in econometric theory  |c John Stachurski 
260 |a Cambridge, MA [u.a.]  |b MIT Press  |c 2016 
300 |a XVII, 430 S.  |b graph. Darst. 
520 |a This book offers a cogent and concise treatment of econometric theory and methods along with the underlying ideas from statistics, probability theory, and linear algebra. It emphasizes foundations and general principles, but also features many solved exercises, worked examples, and code listings. After mastering the material presented, readers will be ready to take on more advanced work in different areas of quantitative economics and to understand papers from the econometrics literature. The book can be used in graduate-level courses on foundational aspects of econometrics or on fundamental statistical principles. It will also be a valuable reference for independent study. One distinctive aspect of the text is its integration of traditional topics from statistics and econometrics with modern ideas from data science and machine learning; readers will encounter ideas that are driving the current development of statistics and increasingly filtering into econometric methodology. The text treats programming not only as a way to work with data but also as a technique for building intuition via simulation. Many proofs are followed by a simulation that shows the theory in action. As a primer, the book offers readers an entry point into the field, allowing them to see econometrics as a whole rather than as a profusion of apparently unrelated ideas. 
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992 |a CONTENTS PREFACE XV COMMON SYMBOLS XVII 1 INTRODUCTION 1 1.1 THE NATURE OF ECONOMETRICS 1 1.2 DATA VERSUS THEORY 3 1.3 COMMENTS ON THE LITERATURE 5 L4 FURTHER READING 5 1 BACKGROUND 7 2 VECTOR SPACES 9 2.1 VECTORS AND VECTOR SPACE 9 2.1.1 VECTORS 9 2.1.2 LINEAR COMBINATIONS AND SPAN 14 2.1.3 LINEAR INDEPENDENCE 17 2.1.4 LINEAR SUBSPACES 20 2.1.5 BASES AND DIMENSION 21 2.1.6 LINEAR MAPS 23 2.1.7 LINEAR INDEPENDENCE AND BIJECTIONS 25 2.2 ORTHOGONALITY 27 2.2.1 DEFINITION AND BASIC PROPERTIES 27 2.2.2 THE ORTHOGONAL PROJECTION THEOREM 29 2.2.3 PROJECTION AS A MAPPING 30 2.2.4 THE RESIDUAL PROJECTION 32 2.3 FURTHER READING 34 2.4 EXERCISES 35 VII CONTENTS VIII 2.4.1 SOLUTIONS TO SELECTED EXERCISES 37 LINEAR ALGEBRA AND MATRICES 45 3.1 MATRICES AND LINEAR EQUATIONS 45 3.1.1 BASIC DEFINITIONS 45 3.1.2 MATRICES AS MAPS 48 3.1.3 SQUARE MATRICES AND INVERTIBILITY 50 3.1.4 DETERMINANTS 52 3.2 PROPERTIES OF MATRICES 53 3.2.1 DIAGONAL AND TRIANGULAR MATRICES 53 3.2.2 TRACE, TRANSPOSE, AND SYMMETRY 54 3.2.3 EIGENVALUES AND EIGENVECTORS 55 3.2.4 QUADRATIC FORMS 57 3.3 PROJECTION AND DECOMPOSITION 60 3.3.1 PROJECTION MATRICES 60 3.3.2 OVERDETERMINED SYSTEMS OF EQUATIONS 62 3.3.3 QR DECOMPOSITION 64 3.3.4 DIAGONALIZATION AND SPECTRAL THEORY 65 3.3.5 NORMS AND CONTINUITY 67 3.4 FURTHER READING 70 3.5 EXERCISES 70 3.5.1 SOLUTIONS TO SELECTED EXERCISES 73 FOUNDATIONS OF PROBABILITY 79 4.1 PROBABILISTIC MODELS 79 4.1.1 SAMPLE SPACES AND EVENTS 79 4.1.2 PROBABILITIES 83 4.1.3 RANDOM VARIABLES 89 4.1.4 EXPECTATIONS 93 4.1.5 MOMENTS AND CO-MOMENTS 97 4.2 DISTRIBUTIONS 99 4.2.1 DEFINING DISTRIBUTIONS ON R 100 4.2.2 DENSITIES AND PMFS 103 4.2.3 INTEGRATING WITH DISTRIBUTIONS 108 4.2.4 DISTRIBUTIONS OF RANDOM VARIABLES 110 4.2.5 EXPECTATIONS FROM DISTRIBUTIONS 112 4.2.6 QUANTILE FUNCTIONS 113 4.3 FURTHER READING 116 4.4 EXERCISES 116 4.4.1 SOLUTIONS TO SELECTED EXERCISES 118 5 MODELING DEPENDENCE 125 5.1 RANDOM VECTORS AND MATRICES 125 5.1.1 RANDOM VECTORS 125 
992 |a 5.1.2 MULTIVARIATE DISTRIBUTIONS 127 5.1.3 DISTRIBUTIONS OF RANDOM VECTORS 132 5.1.4 INDEPENDENCE 135 5.1.5 COPULAS 138 5.1.6 PROPERTIES OF NAMED DISTRIBUTIONS 140 5.2 CONDITIONING AND EXPECTATION 141 5.2.1 CONDITIONAL DISTRIBUTIONS 1.41 5.2.2 THE SPACE L 2 142 5.2.3 PROJECTIONS IN LO 145 5.2.4 MEASURABILITY 148 5.2.5 CONDITIONAL EXPECTATION 150 5.2.6 THE VECTOR CASE 153 5.3 FURTHER READING 154 5.4 EXERCISES 154 5.4.1 SOLUTIONS TO SELECTED EXERCISES 156 6 ASYMPTOTICS 161 6.1 LLN AND CLT 161 6.1.1 CONVERGENCE OF RANDOM VECTORS 161 6.1.2 THE LAW OF LARGE NUMBERS 163 6.1.3 CONVERGENCE IN DISTRIBUTION 165 6.1.4 THE CENTRAL LIMIT THEOREM 168 6.2 EXTENSIONS 169 6.2.1 CONVERGENCE OF RANDOM MATRICES 170 6.2.2 VECTOR-VALUED LLNS AND CLTS 171 6.2.3 THE DELTA METHOD 173 6.3 FURTHER READING 174 6.4 EXERCISES 174 6.4.1 SOLUTIONS TO SELECTED EXERCISES 175 7 FURTHER TOPICS IN PROBABILITY 177 7.1 STOCHASTIC PROCESSES 177 7.1.1 STATIONARITV AND ERGODICITY 178 7.1.2 STOCHASTIC RECURSIVE SEQUENCES 179 7.2 MARKOV PROCESSES 184 7.2.1 THE MARKOV ASSUMPTION 184 7.2.2 MARGINAL AND JOINT DISTRIBUTIONS 188 CONTENTS IX X CONTENTS 7.23 STATIONARITV OF MARKOV PROCESSES 190 J 7.2.4 ASYMPTOTICS OF MARKOV PROCESSES 193 7.2.5 THE LINEAR CASE 196 7.3 MARTINGALES 197 7.3.1 DEFINITIONS 197 7.3.2 MARTINGALE DIFFERENCE LLN AND CLT 199 7.4 SIMULATION 200 7.4.1 INVERSE TRANSFORMS 200 7.4.2 MARKOV CHAIN MONTE CARLO 201 7.5 FURTHER READING 206 7.6 EXERCISES 206 7.6.1 SOLUTIONS TO SELECTED EXERCISES 207 II FOUNDATIONS OF STATISTICS 211 8 ESTIMATORS 213 8.1 THE ESTIMATION PROBLEM 213 8 . 1.1 DEFINITIONS 213 8 . 1.2 STATISTICS AND ESTIMATORS 216 8.1.3 EMPIRICAL DISTRIBUTIONS 219 8.2 ESTIMATION PRINCIPLES 222 8 . 2.1 THE SAMPLE ANALOGUE PRINCIPLE 222 8.2.2 EMPIRICAL RISK MINIMIZATION 225 8.2.3 THE CHOICE OF HYPOTHESIS SPACE 228 8.3 SOME PARAMETRIC METHODS 233 8.3.1 MAXIMUM LIKELIHOOD 234 8.3.2 MAXIMUM LIKELIHOOD VIA ERM 238 8.3.3 THE METHOD OF MOMENTS AND GMM 239 8.3.4 BAYESIAN ESTIMATION 241 
992 |a 8.4 FURTHER READING 244 8.5 EXERCISES 244 8.5.1 SOLUTIONS TO SELECTED EXERCISES 245 9 PROPERTIES OF ESTIMATORS 247 9.1 SAMPLING DISTRIBUTIONS 247 9.1.1 ESTIMATORS AS RANDOM ELEMENTS 247 9.1.2 SAMPLING DISTRIBUTIONS 248 9.1.3 THE BOOTSTRAP 251 9.2 EVALUATING ESTIMATORS 255 CONTENTS XI 9.2.1 BIAS 256 9.2.2 VARIANCE 257 9.2.3 VARIANCE VERSUS BIAS 259 9.2.4 ASYMPTOTIC PROPERTIES 262 9.2.5 DECISION THEORY 265 9.3FURTHER READING 270 9.4 EXERCISES 270 9.4.1 SOLUTIONS TO SELECTED EXERCISES 272 10 CONFIDENCE INTERVALS AND TESTS 275 10.1CONFIDENCE SETS 275 10.1.1 FINITE SAMPLE CONFIDENCE SETS 276 10.1.2 ASYMPTOTIC METHODS277 10.1.3 A NONPARAMETRIC EXAMPLE 279 10.2 HYPOTHESIS TESTS280 10.2.1 CONSTRUCTING TESTS 282 10.2.2 CHOOSING CRITICAL VALUES 284 10.2.3 ASYMPTOTIC TESTS286 10.2.4 ACCEPTING THE NULL?289 10.2.5 STATISTICAL TESTS IN ECONOMICS 293 10.3 FURTHER READING 294 10.4 EXERCISES 295 10.4.1 SOLUTIONS TO SELECTED EXERCISES 296 III ECONOMETRIC MODELS 297 11 REGRESSION299 11.1LINEAR REGRESSION 299 11.1.1 THE SETUP 299 11.1.2 THE LEAST SQUARES ESTIMATOR 301 11.1.3 OUT-OF-SAMPLE FIT 304 11.1.4 IN-SAMPLE FIT 306 11.2 THE GEOMETRY OF LEAST SQUARES 308 11.2.1 TRANSFORMATIONS AND BASIS FUNCTIONS308 11.2.2 THE FRISCH-VVAUGH-LOVELL THEOREM 311 11.2.3 CENTERED OBSERVATIONS 314 11.3 FURTHER READING 315 11.4 EXERCISES 315 11.4.1 SOLUTIONS TO SELECTED EXERCISES 317 12 ORDINARY LEAST SQUARES 323 12.1 ESTIMATION UNDER OLS 323 12.1.1 ASSUMPTIONS 323 12.1.2 THE OLS ESTIMATORS 325 12.1.3 FINITE SAMPLE PROPERTIES 327 12.1.4 INFERENCE WITH NORMAL ERRORS 331 12.2 PROBLEMS AND EXTENSIONS 338 12.2.1 NONSPHERICAL ERRORS 338 12.2.2 BIAS 340 12.2.3 INSTRUMENTAL VARIABLES 343 12.2.4 CAUSALITY 345 12.3 FURTHER READING 347 12.4 EXERCISES 347 12.4.1 SOLUTIONS TO SELECTED EXERCISES 349 13 LARGE SAMPLES AND DEPENDENCE 355 13.1 LARGE SAMPLE LEAST SQUARES 355 13.1.1 SETUP AND ASSUMPTIONS 355 13.1.2 CONSISTENCY 358 13.1.3 ASYMPTOTIC NORMALITY OF /5 359 13.1.4 LARGE SAMPLE TESTS 361 
992 |a 13.2 MLE FOR MARKOV PROCESSES 363 13.2.1 THE LIKELIHOOD FUNCTION 363 13.2.2 THE NEWTON-RAPHSON ALGORITHM 365 13.3 FURTHER READING 370 13.4 EXERCISES 370 13.4.1 SOLUTIONS TO SELECTED EXERCISES 372 14 REGULARIZATION 377 14.1 NONPARAMETRIC DENSITY ESTIMATION 377 14.1.1 INTRODUCTION 377 14.1.2 KERNEL DENSITY ESTIMATION 379 14.1.3 THEORY 381 14.1.4 COMMENTARY 386 J 14.2 CONTROLLING COMPLEXITY 386 14.2.1 RIDGE REGRESSION 387 14.2.2 SUBSET SELECTION AND RIDGE REGRESSION 389 14.2.3 BAYESIAN METHODS AND REGULARIZATION 392 14.2.4 CROSS-VALIDATION 395 14.3 FURTHER READING 399 XII CONTENTS CONTENTS 14.4 EXERCISES 399 14.4.1 SOLUTIONS TO SELECTED EXERCISES 400 IV APPENDIX 403 15 APPENDIX 405 15.1 SETS 405 15.1.1 CARTESIAN PRODUCTS 408 15.2 FUNCTIONS 408 15.2.1 PREIMAGE OF SETS 411 15.3 CARDINALITY AND MEASURE 411 15.3.1 LEBESGUE MEASURE AND SETS OF MEASURE ZERO 412 15.4 REAL-VALUED FUNCTIONS 413 15.4.1 SUP AND INF 413 BIBLIOGRAPHY 415 INDEX 425 XIII 

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