Multivariate Statistical Analysis, Second Edition tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn v...
[...]... comments of reviewers of the first edition and colleagues who have used it The comments of v vi Preface to the Second Edition my own students and my long experience in teaching the subject have also been utilized in preparing the Second Edition Narayan C Giri Preface to the First Edition This book is an up-to-date presentation of both theoretical and applied aspects of multivariate analysis using the... Preface to the Second Edition As in the first edition the aim has been to provide an up-to-date presentation of both the theoretical and applied aspects of multivariate analysis using the invariance approach for readers with a basic knowledge of mathematics and statistics at the undergraduate level This new edition updates the original book by adding new results,... earlier books on multivariate statistical inference My long experience teaching multivariate statistical analysis courses in several universities and the comments of my students have also been utilized in writing this volume Invariance is the mathematical term for symmetry with respect to a certain group of transformations As in other branches of mathematics the notion of invariance in statistical inference... theorem, and robustness studies of statistical tests Chapter 4 deals with multivariate normal distributions by means of the probability density function and a simple characterization The second approach simplifies multivariate theory and allows suitable generalization from univariate theory without further analysis This chapter also contains some characterizations of the real multivariate normal distribution,... groups and related results that are useful for the development of invariant statistical test procedures It also contains results on Jacobians of some important transformations that are used in multivariate sampling distributions Chapter 3 is devoted to basic notions of multivariate distributions and the principle of invariance in statistical inference The interrelationship between invariance and sufficiency,... positive part of the James – Stein estimator, Preface to the First Edition ix unbiased estimation of risk, smoother shrinkage estimation of mean with known and unknown covariance matrix are considered here Chapter 6 contains a systematic derivation of basic multivariate sampling distributions for the multivariate normal case, the complex multivariate normal case, and the case of symmetric distributions... spread the materials over two threehour one-semester basic courses on multivariate analysis for statistics graduate students or one three-hour one-semester course for graduate students in nonstatistic majors by proper selection of materials according to need Narayan C Giri Contents Preface to the Second Edition Preface to the First Edition v vii 1 VECTOR AND MATRIX ALGEBRA 1.0 Introduction 1.1 Vectors... Exercises References 41 41 41 44 49 55 56 57 58 58 59 61 63 65 4 PROPERTIES OF MULTIVARIATE DISTRIBUTIONS 4.0 Introduction 4.1 Multivariate Normal Distribution (Classical Approach) 4.2 Complex Multivariate Normal Distribution 4.3 Symmetric Distribution: Its Properties and Characterizations 4.4 Concentration Ellipsoid and Axes (Multivariate Normal) 4.5 Regression, Multiple and Partial Correlation 4.6 Cumulants... of the general class of statistical tests It is now established as a very powerful tool for proving the optimality of many statistical test procedures It is a generally accepted principle that if a problem with a unique solution is invariant under a certain transformation, then the solution should be invariant under that transformation Another compelling reason for discussing multivariate analysis through... the case of symmetric distributions Chapter 7 deals with tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimal properties, tests of hypotheses concerning the subvectors of m in multivariate normal, tests of mean in multivariate complex normal and symmetric distributions, and the robustness of the T 2 -test in the family . Sampling Techniques: Second Edition, Revised and Expanded, Ranjan K. Som 149. Multivariate Statistical Analysis, Narayan C. Giri 150. Handbook of the Normal Distribution: Second Edition, Revised. A. Giles The EM Algorithm and Related Statistical Models, edited by Michiko Watanabe and Kazunon Yamaguchi Multivariate Statistical Analysis: Second Edition, Revised and Expanded, Narayan. Regression and Spline Smoothing: Second Edition, Randall L. Eu- bank 158. Asymptotics, Nonparametrics, and Time Series, edited by Subir Ghosh 159. Multivariate Analysis, Design of Experiments,