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This volume features selected, refereed papers on various aspects of statistics, matrix theory and its applications to statistics, as well as related numerical linear algebra topics and numerical solution methods, which are relevant for problems arising in statistics and in big data. The contributions were originally presented at the 25th International Workshop on Matrices and Statistics (IWMS 2016), held in Funchal (Madeira), Portugal on June 6-9, 2016. The IWMS workshop series brings together statisticians, computer scientists, data scientists and mathematicians, helping them better understand each other’s tools, and fostering new collaborations at the interface of matrix theory and statistics.
Mathematical statistics. --- Matrix theory. --- Data mining. --- Statistics. --- Distribution (Probability theory. --- Computer science. --- Statistical Theory and Methods. --- Linear and Multilinear Algebras, Matrix Theory. --- Data Mining and Knowledge Discovery. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Probability Theory and Stochastic Processes. --- Probability and Statistics in Computer Science. --- Informatics --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistics . --- Algebra. --- Probabilities. --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical analysis --- Algebras, Linear. --- Biometry. --- Computer science --- Linear Algebra. --- Biostatistics. --- Probability Theory. --- Mathematics. --- Computer mathematics --- Electronic data processing --- Biological statistics --- Biology --- Biometrics (Biology) --- Biostatistics --- Biomathematics --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology
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In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.
Linear models (Statistics) --- Matrix analytic methods --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Models, Linear (Statistics) --- Statistics. --- Statistical Theory and Methods. --- Mathematical models --- Mathematical statistics --- Statistics --- Mathematical statistics. --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics
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This is an unusual book because it contains a great deal of formulas. Hence it is a blend of monograph, textbook, and handbook. It is intended for students and researchers who need quick access to useful formulas appearing in the linear regression model and related matrix theory. This is not a regular textbook - this is supporting material for courses given in linear statistical models. Such courses are extremely common at universities with quantitative statistical analysis programs.
Linear regression. --- Mathematics. --- Matrix theory. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Linear systems --- Mathematical models. --- Formulae. --- Formulas (Mathematics) --- Mathematical formulae --- Mathematical formulas --- Systems, Linear --- Statistics. --- Algebra. --- Econometrics. --- Statistical Theory and Methods. --- Linear and Multilinear Algebras, Matrix Theory. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Differential equations, Linear --- System theory --- Mathematical statistics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Economics, Mathematical --- Statistics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistics . --- Mathematical analysis
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In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple tricks which simplify and clarify the treatment of a problem both for the student and for the professor. Of course, the concept of a trick is not uniquely defined by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.
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This is an unusual book because it contains a great deal of formulas. Hence it is a blend of monograph, textbook, and handbook. It is intended for students and researchers who need quick access to useful formulas appearing in the linear regression model and related matrix theory. This is not a regular textbook - this is supporting material for courses given in linear statistical models. Such courses are extremely common at universities with quantitative statistical analysis programs.
Statistical science --- Quantitative methods (economics) --- Economics --- Algebra --- Mathematical statistics --- Business economics --- algebra --- matrices --- economie --- statistiek --- econometrie --- wiskunde --- statistisch onderzoek
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This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.
Combinatorial analysis. --- Graph connectivity. --- Laplacian matrices. --- Matrices. --- Matrices --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Linear systems --- Systems, Linear --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Mathematics. --- Matrix theory. --- Algebra. --- Statistics. --- Linear and Multilinear Algebras, Matrix Theory. --- Statistical Theory and Methods. --- Differential equations, Linear --- System theory --- Algebra, Abstract --- Algebra, Universal --- Mathematical statistics. --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Mathematical analysis --- Matrix inversion.
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This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.
Algebras, Linear. --- Probabilities. --- Statistics. --- Graph theory. --- Stochastic processes. --- Game theory. --- Linear Algebra. --- Probability Theory. --- Statistical Theory and Methods. --- Graph Theory. --- Stochastic Processes. --- Game Theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Random processes --- Probabilities --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Extremal problems --- Àlgebra lineal --- Probabilitats --- Estadística
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