Mathematics for econometrics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 240 S. |
| ISBN: | 0387989951 |
Staff View
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| 100 | 1 | |a Dhrymes, Phoebus J. |d 1932-2016 |e Verfasser |0 (DE-588)108367622 |4 aut | |
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Record in the Search Index
| _version_ | 1804128064176652288 |
|---|---|
| adam_text | Titel: Mathematics for econometrics
Autor: Dhrymes, Phoebus J
Jahr: 2000
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
xii
CONTENTS
2.9.1 Kronecker Product Matrices...............* *
2.10 Orthogonal Matrices.......................66
2.11 Symmetric Matrices........................^
2.12 Idempotent Matrices.......................77
2.13 Semidefinite and Definite Matrices ...............79
3 Systems of Linear Equations 93
no
3.1 Introduction............................yo
3.2 The c-, s-, and g-Inverses.....................
3.3 Properties of the Generalized Inverse..............9
3.4 Linear Equations and Pseudoinverses..............165
3.5 Approximate Solutions......................H6
4 Matrix Vectorization H7
4.1 Introduction............................H7
4.2 Vectorization of Matrices.....................H®
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
CONTENTS xiii
7 Asymptotic Expansions 185
7.1 Introduction............................185
7.2 Preliminaries ...........................186
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
|
| any_adam_object | 1 |
| author | Dhrymes, Phoebus J. 1932-2016 |
| author_GND | (DE-588)108367622 |
| author_facet | Dhrymes, Phoebus J. 1932-2016 |
| author_role | aut |
| author_sort | Dhrymes, Phoebus J. 1932-2016 |
| author_variant | p j d pj pjd |
| building | Verbundindex |
| bvnumber | BV013296625 |
| callnumber-first | Q - Science |
| callnumber-label | QA184 |
| callnumber-raw | QA184.D53 2000 |
| callnumber-search | QA184.D53 2000 |
| callnumber-sort | QA 3184 D53 42000 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 300 SK 970 SK 980 |
| ctrlnum | (OCoLC)43930010 (DE-599)BVBBV013296625 |
| dewey-full | 512/.521 512/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.5 21 512/.5 |
| dewey-search | 512/.5 21 512/.5 |
| dewey-sort | 3512 15 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| spelling | Dhrymes, Phoebus J. 1932-2016 Verfasser (DE-588)108367622 aut Mathematics for econometrics Phoebus J. Dhrymes 3. ed. New York [u.a.] Springer 2000 XII, 240 S. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Algèbre linéaire rasuqam Econometrie gtt Lineaire algebra gtt Matrice rasuqam Économétrie Économétrie rasuqam Algebras, Linear Econometrics Mathematik (DE-588)4037944-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Ökonometrie (DE-588)4132280-0 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 Überarbeitet als Fourth edition 2013 978-1-4614-8144-7 (DE-604)BV046031488 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009064508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dhrymes, Phoebus J. 1932-2016 Mathematics for econometrics Algèbre linéaire Algèbre linéaire rasuqam Econometrie gtt Lineaire algebra gtt Matrice rasuqam Économétrie Économétrie rasuqam Algebras, Linear Econometrics Mathematik (DE-588)4037944-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4035811-2 (DE-588)4132280-0 |
| title | Mathematics for econometrics |
| title_auth | Mathematics for econometrics |
| title_exact_search | Mathematics for econometrics |
| title_full | Mathematics for econometrics Phoebus J. Dhrymes |
| title_fullStr | Mathematics for econometrics Phoebus J. Dhrymes |
| title_full_unstemmed | Mathematics for econometrics Phoebus J. Dhrymes |
| title_short | Mathematics for econometrics |
| title_sort | mathematics for econometrics |
| topic | Algèbre linéaire Algèbre linéaire rasuqam Econometrie gtt Lineaire algebra gtt Matrice rasuqam Économétrie Économétrie rasuqam Algebras, Linear Econometrics Mathematik (DE-588)4037944-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Algèbre linéaire Econometrie Lineaire algebra Matrice Économétrie Algebras, Linear Econometrics Mathematik Lineare Algebra Ökonometrie |
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