Multivariate Reduced Rank Regression
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Multivariate Reduced Rank Regression
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Author : Gregory C. Reinsel
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
Multivariate Reduced Rank Regression written by Gregory C. Reinsel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.
Multivariate Reduced Rank Regression
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Author : Raja Velu
language : en
Publisher:
Release Date : 2014-01-15
Multivariate Reduced Rank Regression written by Raja Velu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Multivariate Reduced Rank Regression
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Author : Raja Velu
language : en
Publisher: Springer
Release Date : 1998-09-18
Multivariate Reduced Rank Regression written by Raja Velu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-18 with Mathematics categories.
In the area of multivariate analysis, there are two broad themes that have emerged over time. The analysis typically involves exploring the variations in a set of interrelated variables or investigating the simultaneous relation ships between two or more sets of variables. In either case, the themes involve explicit modeling of the relationships or dimension-reduction of the sets of variables. The multivariate regression methodology and its variants are the preferred tools for the parametric modeling and descriptive tools such as principal components or canonical correlations are the tools used for addressing the dimension-reduction issues. Both act as complementary to each other and data analysts typically want to make use of these tools for a thorough analysis of multivariate data. A technique that combines the two broad themes in a natural fashion is the method of reduced-rank regres sion. This method starts with the classical multivariate regression model framework but recognizes the possibility for the reduction in the number of parameters through a restrietion on the rank of the regression coefficient matrix. This feature is attractive because regression methods, whether they are in the context of a single response variable or in the context of several response variables, are popular statistical tools. The technique of reduced rank regression and its encompassing features are the primary focus of this book. The book develops the method of reduced-rank regression starting from the classical multivariate linear regression model.
Multivariate Reduced Rank Regression
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Author : Raja Velu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Multivariate Reduced Rank Regression written by Raja Velu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
In the area of multivariate analysis, there are two broad themes that have emerged over time. The analysis typically involves exploring the variations in a set of interrelated variables or investigating the simultaneous relation ships between two or more sets of variables. In either case, the themes involve explicit modeling of the relationships or dimension-reduction of the sets of variables. The multivariate regression methodology and its variants are the preferred tools for the parametric modeling and descriptive tools such as principal components or canonical correlations are the tools used for addressing the dimension-reduction issues. Both act as complementary to each other and data analysts typically want to make use of these tools for a thorough analysis of multivariate data. A technique that combines the two broad themes in a natural fashion is the method of reduced-rank regres sion. This method starts with the classical multivariate regression model framework but recognizes the possibility for the reduction in the number of parameters through a restrietion on the rank of the regression coefficient matrix. This feature is attractive because regression methods, whether they are in the context of a single response variable or in the context of several response variables, are popular statistical tools. The technique of reduced rank regression and its encompassing features are the primary focus of this book. The book develops the method of reduced-rank regression starting from the classical multivariate linear regression model.
Modern Multivariate Statistical Techniques
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Author : Alan J. Izenman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-02
Modern Multivariate Statistical Techniques written by Alan J. Izenman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-02 with Mathematics categories.
This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.
Sparse Multivariate Reduced Rank Regression With Covariance Estimation
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Author : Khalif Aly Halani
language : en
Publisher:
Release Date : 2016
Sparse Multivariate Reduced Rank Regression With Covariance Estimation written by Khalif Aly Halani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Multivariate multiple linear regression is multiple linear regression, but with multiple responses. Standard approaches assume that observations from different subjects are uncorrelated and so estimates of the regression parameters can be obtained through separate univariate regressions, regardless of whether the responses are correlated within subjects. There are three main extensions to the simplest model. The first assumes a low rank structure on the coefficient matrix that arises from a latent factor model linking predictors to responses. The second reduces the number of parameters through variable selection. The third allows for correlations between response variables in the low rank model. Chen and Huang propose a new model that falls under the reduced-rank regression framework, employs variable selection, and estimates correlations among error terms. This project reviews their model, describes its implementation, and reports the results of a simulation study evaluating its performance. The project concludes with ideas for further research.
Elements Of Multivariate Time Series Analysis
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Author : Gregory C. Reinsel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-31
Elements Of Multivariate Time Series Analysis written by Gregory C. Reinsel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-31 with Mathematics categories.
Now available in paperback, this book introduces basic concepts and methods useful in the analysis and modeling of multivariate time series data. It concentrates on the time-domain analysis of multivariate time series, and assumes univariate time series analysis, while covering basic topics such as stationary processes and their covariance matrix structure, vector AR, MA, and ARMA models, forecasting, least squares and maximum likelihood estimation for ARMA models, associated likelihood ratio testing procedures.
Reduced Rank Regression
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Author : Heinz Schmidli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Reduced Rank Regression written by Heinz Schmidli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Mathematics categories.
Reduced rank regression is widely used in statistics to model multivariate data. In this monograph, theoretical and data analytical approaches are developed for the application of reduced rank regression in multivariate prediction problems. For the first time, both classical and Bayesian inference is discussed, using recently proposed procedures such as the ECM-algorithm and the Gibbs sampler. All methods are motivated and illustrated by examples taken from the area of quantitative structure-activity relationships (QSAR).
Linear Models In Statistics
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Author : Alvin C. Rencher
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-07
Linear Models In Statistics written by Alvin C. Rencher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-07 with Mathematics categories.
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
International Encyclopedia Of Statistical Science
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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.