Mathematics for econometrics

1. Person: Dhrymes, Phoebus J.
Format: Buch
Sprache: English
Veröffentlicht: New York [u.a.] Springer 2000
Beschreibung: XIII, 240 S. graph. Darst.
Ausgabe: 3. ed., 1. print.
Schlagworte (SWD): Lineare Algebra
Ökonometrie
Schlagworte (SH): Algebras, Linear
Econometrics
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992 |a IMAGE 1 PHOEBUS J. DHRYMES MATHEMATICS FOR ECONOMETRICS THIRD EDITION SPRINGER IMAGE 2 CONTENTS PREFACE TO THE THIRD EDITION V PREFACE TO THE SECOND EDITION VII PREFACE TO THE FIRST EDITION IX 1 VECTORS AND VECTOR SPACES 1 1.1 COMPLEX NUMBERS 1 1.1.1 POLAR FORM OF COMPLEX NUMBERS 3 1.2 VECTORS 5 1.3 VECTOR SPACES 6 1.3.1 BASIS OF A VECTOR SPACE 8 1.4 SUBSPACES OF A VECTOR SPACE 9 2 MATRIX ALGEBRA 11 2.1 BASIC DEFINITIONS 11 2.2 BASIC OPERATIONS 13 2.3 RANK AND INVERSE OF A MATRIX 15 2.3.1 MATRIX INVERSION 16 2.4 HERMITE FORMS AND RANK FACTORIZATION 21 2.4.1 RANK FACTORIZATION 26 2.5 TRACE AND DETERMINANTS 28 2.6 COMPUTATION OF THE INVERSE 37 2.7 PARTITIONED MATRICES 38 2.8 KRONECKER PRODUCTS OF MATRICES 49 2.9 CHARACTERISTIC ROOTS AND VECTORS 52 XI IMAGE 3 XII CONTENTS 2.9.1 KRONECKER PRODUCT MATRICES 65 2.10 ORTHOGONAL MATRICES 66 2.11 SYMMETRIE MATRICES 69 2.12 IDEMPOTENT MATRICES 77 2.13 SEMIDEFINITE AND DEFINITE MATRICES 79 3 SYSTEMS OF LINEAR EQUATIONS 93 3.1 INTRODUCTION 93 3.2 THE C-, S-, AND G-INVERSES 94 3.3 PROPERTIES OF THE GENERALIZED INVERSE 98 3.4 LINEAR EQUATIONS AND PSEUDOINVERSES 105 3.5 APPROXIMATE SOLUTIONS 110 4 MATRIX VECTORIZATION 117 4.1 INTRODUCTION 117 4.2 VECTORIZATION OF MATRICES 118 4.3 LINEARLY RESTRICTED MATRICES 122 4.3.1 RESTRICTED SUBSPACES 126 4.3.2 THE STRUCTURE OF RESTRICTED SUBSPACES 134 4.3.3 PERMUTATION MATRICES AND THE VEC OPERATOR 137 4.3.4 PERMUTATION AND THE VEC OPERATOR . . 144 5 VECTOR AND MATRIX DIFFERENTIATION 146 5.1 INTRODUCTION 146 5.2 DERIVATIVES OF FUNCTIONS OF THE FORM Y = AX 147 5.3 DERIVATIVES OF FUNCTIONS OF THE FORM Y — Z AX 150 5.4 DIFFERENTIATION OF THE TRACE 154 5.5 DIFFERENTIATION OF DETERMINANTS 158 5.6 DIFFERENTIATION OF INVERSE OF A MATRIX 166 6 DIFFERENCE EQUATIONS 168 6.1 THE SCALAR SECOND-ORDER EQUATION 168 6.2 VECTOR DIFFERENCE EQUATIONS 175 6.3 AN APPLICATION TO THE GLSEM 179 IMAGE 4 CONTENTS XIII 7 ASYMPTOTIC EXPANSIONS 185 7.1 INTRODUCTION 185 7.2 PRELIMINARIES 186 
992 |a 7.3 GENERAL BOUNDS ON APPROXIMATIONS 189 7.4 CHARACTERISTIC AND MOMENT GENERATING FUNCTIONS 190 7.5 CF, MGF, MOMENTS, AND CUMULANTS 193 7.5.1 CF, MGF, AND THE EXISTENCE OF MOMENTS 193 7.5.2 CUMULANTS AND CUMULANT GENERATING FUNCTIONS (CGF) 197 7.6 SERIES APPROXIMATION 200 8 APPLICATIONS: THE GLM 202 8.1 INTRODUCTION 202 8.2 THE GLM AND THE LEAST SQUARES ESTIMATOR 203 8.3 PROPERTIES OF THE ESTIMATORS 204 8.4 DISTRIBUTION OF OLS ESTIMATORS 206 8.5 NONSTANDARD ERRORS 212 8.6 ORTHOGONAL REGRESSORS 217 9 APPLICATIONS: THE GLSEM 222 9.1 INTRODUCTION 222 9.2 INCONSISTENCY OF ORDINARY LEAST SQUARES 224 9.3 THE 2SLS ESTIMATOR 226 9.4 AN ALTERNATIVE DERIVATION OF 2SLS AND 3SLS 227 9.4.1 SYSTEMWIDE ESTIMATION 228 9.5 TESTS FOR OVERIDENTIFYING RESTRICTIONS 229 9.6 IDENTIFICATION 231 BIBLIOGRAPHY 236 INDEX 237 ) 

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