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.
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
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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.