Matrix Calculus and Zero-One Matrices

Statistical and Econometric Applications

Author: Darrell A. Turkington

Publisher: Cambridge University Press

ISBN: 9780521022453

Category: Business & Economics

Page: 220

View: 6785

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.

Generalized Vectorization, Cross-Products, and Matrix Calculus

Author: Darrell A. Turkington

Publisher: Cambridge University Press

ISBN: 1107032008

Category: Business & Economics

Page: 267

View: 4040

"This book studies the mathematics behind matrix calculus, and the final chapter looks at applications of matrix calculus in statistics and econometrics"--

Multivariate Statistics: Theory and Applications

Author: Tõnu Kollo

Publisher: World Scientific

ISBN: 9814449415

Category: Mathematics

Page: 180

View: 2289

The book aims to present a wide range of the newest results on multivariate statistical models, distribution theory and applications of multivariate statistical methods. A paper on Pearson–Kotz–Dirichlet distributions by Professor N Balakrishnan contains main results of the Samuel Kotz Memorial Lecture. Extensions of linear models to multivariate exponential dispersion models and Growth Curve models are presented, and several papers on classification methods are included. Applications range from insurance mathematics to medical and industrial statistics and sampling algorithms. Contents:Variable Selection and Post-Estimation of Regression Parameters Using Quasi-Likelihood Approach (S Fallahpour and S E Ahmed)Maximum Likelihood Estimates for Markov-Additive Processes of Arrivals by Aggregated Data (A M Andronov)A Simple and Efficient Method of Estimation of the Parameters of a Bivariate Birnbaum-Saunders Distribution Based on Type-II Censored Samples (N Balakrishnan and X Zhu)Analysis of Contingent Valuation Data with Self-Selected Rounded WTP-Intervals Collected by Two-Steps Sampling Plans (Yu K Belyaev and B Kriström)Optimal Classification of Multivariate GRF Observations (K Dučinskas and L Dreižienė)Multivariate Exponential Dispersion Models (B Jørgensen and J R Martínez)Statistical Inference with the Limited Expected Value Function (M Käärik and H Kadarik)Shrinkage Estimation via Penalized Least Squares in Linear Regression with an Application to Hip Fracture Treatment Costs (A Liski, E P Liski and U Häkkinen)K-Nearest Neighbors as Pricing Tool in Insurance: A Comparative Study (K Pärna, R Kangro, A Kaasik and M Möls)Statistical Study of Factors Affecting Knee Joint Space and Osteophytes in the Population with Early Knee Osteoarthritis (T von Rosen, A E Tamm, A O Tamm and I Traat)Simultaneous Confidence Region for ρ and σ2 in a Multivariate Linear Model with Uniform Correlation Structure (I Žežula and D Klein) Readership: Graduated students and Professional researchers in mathematics. Keywords:Multivariate Distributions;Multivariate Statistical Models;Applications of Multivariate Statistical MethodsKey Features:Among the authors several prominent ones appear: N Balakrishnan, E Ahmed, Y Belyaev, B JorgensenOnly few books are published which are dedicated to the problems of multivariate statistics only thus it valuable for people who work in multivariate statisticsApplications in different areas demonstrate the usefulness of the theory in practice

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3236

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 6803

Books in Print

Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5363

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Matrix differential calculus with applications in statistics and econometrics

Author: Jan R. Magnus,Heinz Neudecker

Publisher: John Wiley & Sons Inc

ISBN: 9780471915164

Category: Business & Economics

Page: 393

View: 7184

This book provides a unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. Divided into six parts, the book begins with a treatment of matrix algebra, discussing the Schur, Jordan, and singular-value decompositions, the Hadamard and Kronecker products, and more. The second section is the theoretical core of the book and presents a thorough development of the theory of differentials. Practically-oriented, part three contains the rules for working with differentials and lists the differentials of important scalar, vector, and matrix functions. The fourth deals with inequalities, such as Cauchy-Schwarz's and Minkowski's, while the fifth section is devoted to applications of matrix differential calculus to the linear regression model. The book closes by detailing maximum likelihood estimation, an ideal source for demonstrating the power of the propagated techniques. Features numerous exercises.

Mathematical Tools for Economics

Author: Darrell A. Turkington

Publisher: Wiley-Blackwell

ISBN: 1405133813

Category: Business & Economics

Page: 378

View: 7083

Designed to demonstrate the essential mathematical concepts—comprehensively and economically—without re-teaching basic material or laboring over superfluous ideas, this text locates the necessary information in a practical economics context. Utilizing clear exposition and dynamic pedagogical features, Mathematical Tools for Economics provides students with the analytical skills they need to better grasp their field of study. A short introduction to mathematics for students of economics Demonstrates essential mathematical concepts necessary for economic analysis, such as matrix algebra and calculus, simultaneous linear equations, and concrete and discrete time Incorporates applications to econometrics and statistics, and includes computational exercises illustrating the methods and concepts discussed in the text Clear explanations and dynamic pedagogical features provide students with the analytical skills they need to better grasp their field of study. Mathematical Tools for Economics is supported by an instructor's manual featuring solutions, available at www.blackwellpublishing.com/turkington

Matrix Algebra

Author: Karim M. Abadir,Jan R. Magnus

Publisher: Cambridge University Press

ISBN: 9780521822893

Category: Business & Economics

Page: 434

View: 9735

A stand-alone textbook in matrix algebra for econometricians and statisticians - advanced undergraduates, postgraduates and teachers.

Mathematics for Econometrics

Author: Phoebus J. Dhrymes

Publisher: Springer Science & Business Media

ISBN: 1461481457

Category: Business & Economics

Page: 419

View: 1589

This book deals with a number of mathematical topics that are of great importance in the study of classical econometrics. There is a lengthy chapter on matrix algebra, which takes the reader from the most elementary aspects to the partitioned inverses, characteristic roots and vectors, symmetric, and orthogonal and positive (semi) definite matrices. The book also covers pseudo-inverses, solutions to systems of linear equations, solutions of vector difference equations with constant coefficients and random forcing functions, matrix differentiation, and permutation matrices. Its novel features include an introduction to asymptotic expansions, and examples of applications to the general-linear model (regression) and the general linear structural econometric model (simultaneous equations).

Arzneimittel und Genussmittel

Author: O. Schmiedeberg

Publisher: BoD – Books on Demand

ISBN: 3846066842

Category: Medical

Page: 148

View: 6523

Nachdruck des Originals von 1912.

Zeitreihenmodelle

Author: Andrew C. Harvey

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486786741

Category: Business & Economics

Page: 396

View: 8749

Gegenstand des Werkes sind Analyse und Modellierung von Zeitreihen. Es wendet sich an Studierende und Praktiker aller Disziplinen, in denen Zeitreihenbeobachtungen wichtig sind.

Statistische Versuchsplanung

Author: Karl Siebertz,David van Bebber,Thomas Hochkirchen

Publisher: Springer Science & Business Media

ISBN: 3642054935

Category: Computers

Page: 328

View: 705

Die statistische Versuchsplanung (Design of Experiment, DoE) ist ein Verfahren zur Analyse von (technischen) Systemen. Dieses Verfahren ist universell einsetzbar und eignet sich sowohl zur Produkt- als auch zur Prozessoptimierung, insbesondere dann, wenn viele Einflussgrößen zu berücksichtigen sind. Hauptanliegen der Autoren ist es, die Planung und Durchführung von systematischen Versuchsreihen mit engem Praxisbezug darzustellen. Industriespezifische Probleme illustrieren sie anhand zahlreicher Fallbeispiele.

Mathematik für Ökonomen

Grundlagen, Methoden und Anwendungen

Author: Alpha C. Chiang,Kevin Wainwright,Harald Nitsch

Publisher: Vahlen

ISBN: 3800645122

Category: Business & Economics

Page: 476

View: 8340

Klar und verständlich: Mathematik für Ökonomen. Für viele Studierende der BWL und VWL hat die Mathematik eine ähnliche Anziehungskraft wie bittere Medizin notwendig, aber extrem unangenehm. Das muss nicht sein. Mit diesem Buch gelingt es jedem, die Methoden zu erlernen. Anhand konkreter ökonomischer Anwendungen wird die Mathematik sehr anschaulich erklärt. Schnelle Lernerfolge Von der Wiederholung des Abiturwissens bis zum Niveau aktueller ökonomischer Lehrbücher wird Schritt für Schritt vorgegangen und alle wichtigen Bereiche der Mathematik systematisch erklärt. Der Lernerfolg stellt sich schnell ein: die klare und ausführliche Darstellung sowie die graphische Unterstützung machen es möglich.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung

Publisher: Springer-Verlag

ISBN: 3642670334

Category: Mathematics

Page: 346

View: 1146

Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1