Wiley Series in Probability and Statistics: Matrix Analysis for Statistics, Third Edition MOBI ebook
9781119092469 English 1119092469 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., This volume provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; the distribution of quadratic forms; and more. The subject matter is presented in a theorem/proof format, and every effort has been made to ease the transition from one topic to another. Proofs are easy to follow, and the author carefully justifies every step. Accessible even for readers with a cursory background in statistics, the text uses examples that are familiar and easy to understand. Key features that make this the ideal introduction to matrix analysis theory and practice include: self-contained chapters for flexibility in topic choice, extensive examples and chapter-end practice exercises, and optional sections for mathematically advanced readers. The third edition includes a new chapter on inequalities. Numerous inequalities (e.g. Cauchy-Schwarz, Hadamard, Jensen's) already appear in the current text, but there are many important ones that are missing and some of these are given in the new chapter. Highlighting this chapter is a fairly substantial section on majorization and some of the inequalities that can be developed from this concept. It also includes a new section in Chapter 2 on oblique projections and their projection matrices and a new section in Chapter 3 on antieigenvalues and antieigenvectors. Finally, new theorems, proofs, examples and problems are included throughout the text.
9781119092469 English 1119092469 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., This volume provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; the distribution of quadratic forms; and more. The subject matter is presented in a theorem/proof format, and every effort has been made to ease the transition from one topic to another. Proofs are easy to follow, and the author carefully justifies every step. Accessible even for readers with a cursory background in statistics, the text uses examples that are familiar and easy to understand. Key features that make this the ideal introduction to matrix analysis theory and practice include: self-contained chapters for flexibility in topic choice, extensive examples and chapter-end practice exercises, and optional sections for mathematically advanced readers. The third edition includes a new chapter on inequalities. Numerous inequalities (e.g. Cauchy-Schwarz, Hadamard, Jensen's) already appear in the current text, but there are many important ones that are missing and some of these are given in the new chapter. Highlighting this chapter is a fairly substantial section on majorization and some of the inequalities that can be developed from this concept. It also includes a new section in Chapter 2 on oblique projections and their projection matrices and a new section in Chapter 3 on antieigenvalues and antieigenvectors. Finally, new theorems, proofs, examples and problems are included throughout the text.