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The Resource Matrix calculus and zero-one matrices : statistical and econometric applications, Darrell A. Turkington, (electronic resource)

Matrix calculus and zero-one matrices : statistical and econometric applications, Darrell A. Turkington, (electronic resource)

Creator
Summary
This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of interest.--
Language
eng
Work
Publication
Extent
1 online resource (xi, 206 pages)
Contents
  • Generalized Vec and Devec Operators
  • Triangular Matrices and Band Matrices
  • Zero-One Matrices
  • Selection Matrices and Permutation Matrices
  • The Commutation Matrix and Generalized Vecs and Devecs of the Commutation Matrix
  • Elimination Matrices L, L
  • Duplication Matrices D, L
  • Results Concerning Zero-One Matrices Associated with an n x n Matrix
  • Shifting Matrices
  • Matrix Calculus
  • Classical Statistical Procedures
  • Some Simple Matrix Calculus Results
  • Matrix Calculus and Zero-One Matrices
  • The Chain Rule and the Product Rule for Matrix Calculus
  • Rules for Vecs of Matrices
  • Rules Developed from the Properties of K[subscript Gn], K[superscript [tau subscript n subscript Gn], and K[superscript [tau subscript n subscript nG]
  • Rules for Scalar Functions of a Matrix
  • Tables of Results
  • Linear-Regression Models
  • The Basic Linear-Regression Model
  • The Linear-Regression Model with Autoregressive Disturbances
  • The Score Vector, the Information Matrix, and the Cramer--Rao Lower Bound
  • Linear-Regression Model with Moving-Average Disturbances
  • Probability Limits Associated with the Information Matrix for the Autoregressive Disturbances Model
  • Probability Limits Associated with the Information Matrix for the Moving-Average Disturbances Model
  • Seemingly Unrelated Regression Equations Models
  • Maximum Likelihood Estimators and Test Procedures
  • Nuisance Parameters
  • Differentiation and Asymptotics
  • Elements of Matrix Algebra
  • Kronecker Products
  • The Vec and the Devec Operators
Isbn
9780511528460
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1017/CBO9780511528460
Instance
Label
Matrix calculus and zero-one matrices : statistical and econometric applications
Title
Matrix calculus and zero-one matrices
Title remainder
statistical and econometric applications
Statement of responsibility
Darrell A. Turkington
Title variation
Matrix Calculus & Zero-One Matrices
Creator
Subject
Language
eng
Summary
This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of interest.--
Assigning source
Provided by publisher
Cataloging source
UkCbUP
http://library.link/vocab/creatorName
Turkington, Darrell A
Index
index present
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Cambridge Social Sciences eBooks
http://library.link/vocab/subjectName
  • Matrices
  • Mathematical statistics
Label
Matrix calculus and zero-one matrices : statistical and econometric applications, Darrell A. Turkington, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1017/CBO9780511528460
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Generalized Vec and Devec Operators
  • Triangular Matrices and Band Matrices
  • Zero-One Matrices
  • Selection Matrices and Permutation Matrices
  • The Commutation Matrix and Generalized Vecs and Devecs of the Commutation Matrix
  • Elimination Matrices L, L
  • Duplication Matrices D, L
  • Results Concerning Zero-One Matrices Associated with an n x n Matrix
  • Shifting Matrices
  • Matrix Calculus
  • Classical Statistical Procedures
  • Some Simple Matrix Calculus Results
  • Matrix Calculus and Zero-One Matrices
  • The Chain Rule and the Product Rule for Matrix Calculus
  • Rules for Vecs of Matrices
  • Rules Developed from the Properties of K[subscript Gn], K[superscript [tau subscript n subscript Gn], and K[superscript [tau subscript n subscript nG]
  • Rules for Scalar Functions of a Matrix
  • Tables of Results
  • Linear-Regression Models
  • The Basic Linear-Regression Model
  • The Linear-Regression Model with Autoregressive Disturbances
  • The Score Vector, the Information Matrix, and the Cramer--Rao Lower Bound
  • Linear-Regression Model with Moving-Average Disturbances
  • Probability Limits Associated with the Information Matrix for the Autoregressive Disturbances Model
  • Probability Limits Associated with the Information Matrix for the Moving-Average Disturbances Model
  • Seemingly Unrelated Regression Equations Models
  • Maximum Likelihood Estimators and Test Procedures
  • Nuisance Parameters
  • Differentiation and Asymptotics
  • Elements of Matrix Algebra
  • Kronecker Products
  • The Vec and the Devec Operators
Control code
CR9780511528460
Dimensions
unknown
Extent
1 online resource (xi, 206 pages)
Form of item
online
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9780511528460
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(OCoLC)708565275
Label
Matrix calculus and zero-one matrices : statistical and econometric applications, Darrell A. Turkington, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1017/CBO9780511528460
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Generalized Vec and Devec Operators
  • Triangular Matrices and Band Matrices
  • Zero-One Matrices
  • Selection Matrices and Permutation Matrices
  • The Commutation Matrix and Generalized Vecs and Devecs of the Commutation Matrix
  • Elimination Matrices L, L
  • Duplication Matrices D, L
  • Results Concerning Zero-One Matrices Associated with an n x n Matrix
  • Shifting Matrices
  • Matrix Calculus
  • Classical Statistical Procedures
  • Some Simple Matrix Calculus Results
  • Matrix Calculus and Zero-One Matrices
  • The Chain Rule and the Product Rule for Matrix Calculus
  • Rules for Vecs of Matrices
  • Rules Developed from the Properties of K[subscript Gn], K[superscript [tau subscript n subscript Gn], and K[superscript [tau subscript n subscript nG]
  • Rules for Scalar Functions of a Matrix
  • Tables of Results
  • Linear-Regression Models
  • The Basic Linear-Regression Model
  • The Linear-Regression Model with Autoregressive Disturbances
  • The Score Vector, the Information Matrix, and the Cramer--Rao Lower Bound
  • Linear-Regression Model with Moving-Average Disturbances
  • Probability Limits Associated with the Information Matrix for the Autoregressive Disturbances Model
  • Probability Limits Associated with the Information Matrix for the Moving-Average Disturbances Model
  • Seemingly Unrelated Regression Equations Models
  • Maximum Likelihood Estimators and Test Procedures
  • Nuisance Parameters
  • Differentiation and Asymptotics
  • Elements of Matrix Algebra
  • Kronecker Products
  • The Vec and the Devec Operators
Control code
CR9780511528460
Dimensions
unknown
Extent
1 online resource (xi, 206 pages)
Form of item
online
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9780511528460
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(OCoLC)708565275

Subject

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