Matrix Differential Calculus With Applications In Statistics And Econometrics

Author : Jan R. Magnus,Heinz Neudecker
Publisher : John Wiley & Sons
Page : 504 pages
File Size : 49,7 Mb
Release : 2019-03-15
Category : Mathematics
ISBN : 9781119541196

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Matrix Differential Calculus with Applications in Statistics and Econometrics by Jan R. Magnus,Heinz Neudecker Pdf

A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.

Author : Jan R. Magnus,Heinz Neudecker
Publisher : John Wiley & Sons
Page : 633 pages
File Size : 54,7 Mb
Release : 2019-03-15
Category : Mathematics
ISBN : 9781119541165

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Matrix Differential Calculus with Applications in Statistics and Econometrics by Jan R. Magnus,Heinz Neudecker Pdf

A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.

Author : Karim M. Abadir,Jan R. Magnus
Publisher : Cambridge University Press
Page : 472 pages
File Size : 47,5 Mb
Release : 2005-08-22
Category : Business & Economics
ISBN : 0521822890

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Matrix Algebra by Karim M. Abadir,Jan R. Magnus Pdf

Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.

Author : Darrell A. Turkington
Publisher : Cambridge University Press
Page : 281 pages
File Size : 42,9 Mb
Release : 2013-02-11
Category : Business & Economics
ISBN : 9781107032002

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Generalized Vectorization, Cross-Products, and Matrix Calculus by Darrell A. Turkington Pdf

This book studies the mathematics behind matrix calculus and the applications of matrix calculus in statistics and econometrics.

Author : Alexander Graham
Publisher : Courier Dover Publications
Page : 145 pages
File Size : 47,7 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9780486824178

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Kronecker Products and Matrix Calculus with Applications by Alexander Graham Pdf

Enhanced by many worked examples, problems, and solutions, this in-depth text is suitable for undergraduates and presents a great deal of information previously only available in specialized and hard-to-find texts. 1981 edition.

Author : Calyampudi Radhakrishna Rao,M. Bhaskara Rao
Publisher : World Scientific
Page : 560 pages
File Size : 46,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9810232683

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Matrix Algebra and Its Applications to Statistics and Econometrics by Calyampudi Radhakrishna Rao,M. Bhaskara Rao Pdf

"I recommend this book for its extensive coverage of topics not easily found elsewhere and for its focus on applications".Zentralblatt MATH"The book is an excellent source on linear algebra, matrix theory and applications in statistics and econometrics, and is unique in many ways. I recommend it to anyone interested in these disciplines, and especially in how they benefit from one another".Statistical Papers, 2000

Author : Darrell A. Turkington
Publisher : Cambridge University Press
Page : 220 pages
File Size : 43,8 Mb
Release : 2002
Category : Business & Economics
ISBN : 9780521807883

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Matrix Calculus and Zero-One Matrices by Darrell A. Turkington Pdf

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.

Author : André I. Khuri
Publisher : John Wiley & Sons
Page : 704 pages
File Size : 42,9 Mb
Release : 2003-04-14
Category : Mathematics
ISBN : 9780471461623

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Advanced Calculus with Applications in Statistics by André I. Khuri Pdf

Designed to help motivate the learning of advanced calculus by demonstrating its relevance in the field of statistics, this successful text features detailed coverage of optimization techniques and their applications in statistics while introducing the reader to approximation theory. The Second Edition provides substantial new coverage of the material, including three new chapters and a large appendix that contains solutions to almost all of the exercises in the book. Applications of some of these methods in statistics are discusses.

Author : Hal Caswell
Publisher : Springer
Page : 308 pages
File Size : 52,7 Mb
Release : 2019-04-02
Category : Social Science
ISBN : 9783030105341

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Sensitivity Analysis: Matrix Methods in Demography and Ecology by Hal Caswell Pdf

This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.

Author : Christian H. Bischof,H. Martin Bücker,Paul Hovland,Uwe Naumann,Jean Utke
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 40,8 Mb
Release : 2008-08-17
Category : Computers
ISBN : 9783540689423

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Advances in Automatic Differentiation by Christian H. Bischof,H. Martin Bücker,Paul Hovland,Uwe Naumann,Jean Utke Pdf

The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic “silver bullet” polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 54,8 Mb
Release : 2007-07-27
Category : Computers
ISBN : 9780387708720

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Matrix Algebra by James E. Gentle Pdf

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Author : James R. Schott
Publisher : John Wiley & Sons
Page : 547 pages
File Size : 48,5 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9781119092483

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Matrix Analysis for Statistics by James R. Schott Pdf

An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

Author : A. K. Gupta,V. L. Girko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 400 pages
File Size : 43,7 Mb
Release : 2019-01-14
Category : Mathematics
ISBN : 9783110916690

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Multidimensional Statistical Analysis and Theory of Random Matrices by A. K. Gupta,V. L. Girko Pdf

This volume contains the papers from the Sixth Eugene Lukacs Symposium on ''Multidimensional Statistical Analysis and Random Matrices'', which was held at the Bowling Green State University, Ohio, USA, 29--30 March 1996. Multidimensional statistical analysis and random matrices have been the topics of great research. The papers presented in this volume discuss many varied aspects of this all-encompassing topic. In particular, topics covered include generalized statistical analysis, elliptically contoured distribution, covariance structure analysis, metric scaling, detection of outliers, density approximation, and circulant and band random matrices.

Author : Akihito Asano
Publisher : Cambridge University Press
Page : 285 pages
File Size : 44,7 Mb
Release : 2012-11-08
Category : Business & Economics
ISBN : 9781107007604

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An Introduction to Mathematics for Economics by Akihito Asano Pdf

A concise, accessible introduction to maths for economics with lots of practical applications to help students learn in context.

Author : Calyampudi Radhakrishna Rao,M. Bhaskara Rao
Publisher : Unknown
Page : 535 pages
File Size : 52,9 Mb
Release : 1998
Category : Econometrics
ISBN : OCLC:245939040

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Matrix Algebra and Its Applications to Statistics and Econometrics by Calyampudi Radhakrishna Rao,M. Bhaskara Rao Pdf