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Matrix calculus and zero-one matrices : = statistical and econometric applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Matrix calculus and zero-one matrices :/ Darrell A. Turkington.
其他題名:	statistical and econometric applications /
其他題名:	Matrix Calculus & Zero-One Matrices
作者:	Turkington, Darrell A.,
面頁冊數:	1 online resource (xi, 206 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Mathematical statistics. -
電子資源:	https://doi.org/10.1017/CBO9780511528460
ISBN:	9780511528460 (ebook)

Matrix calculus and zero-one matrices : = statistical and econometric applications /
Turkington, Darrell A.,

Matrix calculus and zero-one matrices :statistical and econometric applications /Matrix Calculus & Zero-One MatricesDarrell A. Turkington. - 1 online resource (xi, 206 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Classical Statistical Procedures --

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.

ISBN: 9780511528460 (ebook)Subjects--Topical Terms:

527941
Mathematical statistics.

LC Class. No.: QA188 / .T865 2002

Dewey Class. No.: 512.9/434

Matrix calculus and zero-one matrices : = statistical and econometric applications /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $t Classical Statistical Procedures -- $t The Score Vector, the Information Matrix, and the Cramer--Rao Lower Bound -- $t Maximum Likelihood Estimators and Test Procedures -- $t Nuisance Parameters -- $t Differentiation and Asymptotics -- $t Elements of Matrix Algebra -- $t Kronecker Products -- $t The Vec and the Devec Operators -- $t Generalized Vec and Devec Operators -- $t Triangular Matrices and Band Matrices -- $t Zero-One Matrices -- $t Selection Matrices and Permutation Matrices -- $t The Commutation Matrix and Generalized Vecs and Devecs of the Commutation Matrix -- $t Elimination Matrices L, L -- $t Duplication Matrices D, L -- $t Results Concerning Zero-One Matrices Associated with an n x n Matrix -- $t Shifting Matrices -- $t Matrix Calculus -- $t Some Simple Matrix Calculus Results -- $t Matrix Calculus and Zero-One Matrices -- $t The Chain Rule and the Product Rule for Matrix Calculus -- $t Rules for Vecs of Matrices -- $t Rules Developed from the Properties of K[subscript Gn], K[superscript [tau subscript n subscript Gn], and K[superscript [tau subscript n subscript nG] -- $t Rules for Scalar Functions of a Matrix -- $t Tables of Results -- $t Linear-Regression Models -- $t The Basic Linear-Regression Model -- $t The Linear-Regression Model with Autoregressive Disturbances -- $t Linear-Regression Model with Moving-Average Disturbances -- $t Probability Limits Associated with the Information Matrix for the Autoregressive Disturbances Model -- $t Probability Limits Associated with the Information Matrix for the Moving-Average Disturbances Model -- $t Seemingly Unrelated Regression Equations Models.
520 $a 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.
650 0 $a Mathematical statistics. $3 527941
650 0 $a Matrices. $3 528174
776 0 8 $i Print version: $z 9780521807883
856 4 0 $u https://doi.org/10.1017/CBO9780511528460