Reduced Rank Regression With Structured Residuals

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.

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.

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).

This volume presents a selection of research papers on various topics at the interface of statistics and computer science. Emphasis is put on the practical applications of statistical methods in various disciplines, using machine learning and other computational methods. The book covers fields of research including the design of experiments, computational statistics, music data analysis, statistical process control, biometrics, industrial engineering, and econometrics. Gathering innovative, high-quality and scientifically relevant contributions, the volume was published in honor of Claus Weihs, Professor of Computational Statistics at TU Dortmund University, on the occasion of his 66th birthday.

Winner of the 2015 Sugiyama Meiko Award (Publication Award) of the Behaviormetric Society of JapanDeveloped by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured componen

In multivariate data analysis, regression techniques predict one set of variables from another while principal component analysis (PCA) finds a subspace of minimal dimensionality that captures the largest variability in the data. How can regression analysis and PCA be combined in a beneficial way? Why and when is it a good idea to combine them? Wha