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: 9520

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: 9030

"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: 9964

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

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Matrix Algebra and Its Applications to Statistics and Econometrics

Author: Calyampudi Radhakrishna Rao,M. Bhaskara Rao

Publisher: World Scientific

ISBN: 9789810232689

Category: Mathematics

Page: 535

View: 4708

"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

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: 4153

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: 1405133805

Category: Business & Economics

Page: 380

View: 6671

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

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: 5424

Books in Print

Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4576

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.

Mathematics for Econometrics

Author: Phoebus J. Dhrymes

Publisher: Springer Science & Business Media

ISBN: 1461481457

Category: Business & Economics

Page: 419

View: 1870

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).

Hands-on Matrix Algebra Using R

Active and Motivated Learning with Applications

Author: Hrishikesh D. Vinod

Publisher: World Scientific

ISBN: 9814313688

Category: Mathematics

Page: 329

View: 6261

Teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. This book provides an overview of matrix theory without being bogged down in proofs or tedium.

Forthcoming Books

Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3547

Microeconometrics

Methods and Applications

Author: A. Colin Cameron,Pravin K. Trivedi

Publisher: Cambridge University Press

ISBN: 1139444867

Category: Business & Economics

Page: N.A

View: 7294

This book provides the most comprehensive treatment to date of microeconometrics, the analysis of individual-level data on the economic behavior of individuals or firms using regression methods for cross section and panel data. The book is oriented to the practitioner. A basic understanding of the linear regression model with matrix algebra is assumed. The text can be used for a microeconometrics course, typically a second-year economics PhD course; for data-oriented applied microeconometrics field courses; and as a reference work for graduate students and applied researchers who wish to fill in gaps in their toolkit. Distinguishing features of the book include emphasis on nonlinear models and robust inference, simulation-based estimation, and problems of complex survey data. The book makes frequent use of numerical examples based on generated data to illustrate the key models and methods. More substantially, it systematically integrates into the text empirical illustrations based on seven large and exceptionally rich data sets.

Matrix Algebra

Author: Karim M. Abadir,Jan R. Magnus

Publisher: Cambridge University Press

ISBN: 9780521822893

Category: Business & Economics

Page: 434

View: 3918

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

Methods of Multivariate Analysis

Author: Alvin C. Rencher,William F. Christensen

Publisher: John Wiley & Sons

ISBN: 1118391675

Category: Mathematics

Page: 800

View: 3089

Praise for the Second Edition "This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere." —IIE Transactions Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including: Confirmatory Factor Analysis Classification Trees Dynamic Graphics Transformations to Normality Prediction for Multivariate Multiple Regression Kronecker Products and Vec Notation New exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code. Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.

The R Book

Author: Michael J. Crawley

Publisher: John Wiley & Sons

ISBN: 1118448960

Category: Mathematics

Page: 1080

View: 856

Hugely successful and popular text presenting an extensive and comprehensive guide for all R users The R language is recognized as one of the most powerful and flexible statistical software packages, enabling users to apply many statistical techniques that would be impossible without such software to help implement such large data sets. R has become an essential tool for understanding and carrying out research. This edition: Features full colour text and extensive graphics throughout. Introduces a clear structure with numbered section headings to help readers locate information more efficiently. Looks at the evolution of R over the past five years. Features a new chapter on Bayesian Analysis and Meta-Analysis. Presents a fully revised and updated bibliography and reference section. Is supported by an accompanying website allowing examples from the text to be run by the user. Praise for the first edition: ‘…if you are an R user or wannabe R user, this text is the one that should be on your shelf. The breadth of topics covered is unsurpassed when it comes to texts on data analysis in R.’ (The American Statistician, August 2008) ‘The High-level software language of R is setting standards in quantitative analysis. And now anybody can get to grips with it thanks to The R Book…’ (Professional Pensions, July 2007)

Applied Econometrics with SAS

Modeling Demand, Supply, and Risk

Author: Barry K. Goodwin,A. Ford Ramsey,Jan Chvosta

Publisher: SAS Institute

ISBN: 1635260507

Category: Computers

Page: 180

View: 1576

Using Applied Econometrics with SAS: Modeling Demand, Supply, and Risk, you will quickly master SAS applications for implementing and estimating standard models in the field of econometrics. This guide introduces you to the major theories underpinning applied demand and production economics. For each of its three main topics—demand, supply, and risk—a concise theoretical orientation leads directly into consideration of specific economic models and econometric techniques, collectively covering the following: Double-log demand systems Linear expenditure systems Almost ideal demand systems Rotterdam models Random parameters logit demand models Frequency-severity models Compound distribution models Cobb-Douglas production functions Translogarithmic cost functions Generalized Leontief cost functions Density estimation techniques Copula models SAS procedures that facilitate estimation of demand, supply, and risk models include the following, among others: PROC MODEL PROC COPULA PROC SEVERITY PROC KDE PROC LOGISTIC PROC HPCDM PROC IML PROC REG PROC COUNTREG PROC QLIM An empirical example, SAS programming code, and a complete data set accompany each econometric model, empowering you to practice these techniques while reading. Examples are drawn from both major scholarly studies and business applications so that professors, graduate students, government economic researchers, agricultural analysts, actuaries, and underwriters, among others, will immediately benefit. This book is part of the SAS Press program.