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Mathematical statistics --- Random variables --- Distribution (Probability theory) --- Multivariate analysis --- Méthode statistique --- Statistical methods --- -Multivariate analysis --- -Random variables --- -519.2 --- Chance variables --- Stochastic variables --- Probabilities --- Variables (Mathematics) --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- Distribution functions --- Frequency distribution --- Characteristic functions --- Problems, exercises, etc --- Probability. Mathematical statistics --- Problems, exercises, etc. --- 519.2 Probability. Mathematical statistics --- 519.2 --- Random variables - Problems, exercises, etc. --- Distribution (Probability theory) - Problems, exercises, etc. --- Multivariate analysis - Problems, exercises, etc.
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Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.
Mathematical statistics. --- Matrices. --- Multivariate analysis. --- Multivariate analysis -- Problems, exercises, etc. --- Singular value decomposition --- Matrix inversion --- Algebras, Linear --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Statistics --- Decomposition method. --- Matrix inversion. --- Algebras, Linear. --- Linear algebra --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Method, Decomposition --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Statistics. --- Statistics, general. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Linear operators --- Matrices --- Operations research --- Programming (Mathematics) --- System analysis --- Algebra, Abstract --- Generalized inverses --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistics .
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Remarkable advances in computation and data storage and the ready availability of huge data sets have been the keys to the growth of the new disciplines of data mining and machine learning, while the enormous success of the Human Genome Project has opened up the field of bioinformatics. These exciting developments, which led to the introduction of many innovative statistical tools for high-dimensional data analysis, are described here in detail. The author takes a broad perspective; for the first time in a book on multivariate analysis, nonlinear methods are discussed in detail as well as linear methods. Techniques covered range from traditional multivariate methods, such as multiple regression, principal components, canonical variates, linear discriminant analysis, factor analysis, clustering, multidimensional scaling, and correspondence analysis, to the newer methods of density estimation, projection pursuit, neural networks, multivariate reduced-rank regression, nonlinear manifold learning, bagging, boosting, random forests, independent component analysis, support vector machines, and classification and regression trees. Another unique feature of this book is the discussion of database management systems. This book is appropriate for advanced undergraduate students, graduate students, and researchers in statistics, computer science, artificial intelligence, psychology, cognitive sciences, business, medicine, bioinformatics, and engineering. Familiarity with multivariable calculus, linear algebra, and probability and statistics is required. The book presents a carefully-integrated mixture of theory and applications, and of classical and modern multivariate statistical techniques, including Bayesian methods. There are over 60 interesting data sets used as examples in the book, over 200 exercises, and many color illustrations and photographs. Alan J. Izenman is Professor of Statistics and Director of the Center for Statistical and Information Science at Temple University. He has also been on the faculties of Tel-Aviv University and Colorado State University, and has held visiting appointments at the University of Chicago, the University of Minnesota, Stanford University, and the University of Edinburgh. He served as Program Director of Statistics and Probability at the National Science Foundation and was Program Chair of the 2007 Interface Symposium on Computer Science and Statistics with conference theme of Systems Biology. He is a Fellow of the American Statistical Association. .
Statistics. --- Statistical Theory and Methods. --- Probability and Statistics in Computer Science. --- Data Mining and Knowledge Discovery. --- Pattern Recognition. --- Computational Biology/Bioinformatics. --- Signal, Image and Speech Processing. --- Computer science. --- Data mining. --- Optical pattern recognition. --- Bioinformatics. --- Mathematical statistics. --- Statistique --- Informatique --- Exploration de données (Informatique) --- Reconnaissance optique des formes (Informatique) --- Bio-informatique --- Statistique mathématique --- Multivariate analysis --- Multivariate analysis. --- Multivariate analysis -- Problems, exercises, etc. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- -Multivariate analysis --- -519.535 --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices --- Electronic information resources --- E-books --- Mathematics. --- Pattern recognition. --- Computer software. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Mathematical Software. --- Distribution (Probability theory. --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Informatics --- Science --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Software, Computer --- Computer systems --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Statistics . --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Risk --- Multivariate analysis - Problems, exercises, etc. --- Pattern perception.
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