Sparse Multivariate Reduced Rank Regression With Covariance Estimation
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Sparse Multivariate Reduced-Rank Regression with Covariance Estimation
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.
Multivariate Reduced-Rank Regression
Author: Gregory C. Reinsel
language: en
Publisher: Springer Nature
Release Date: 2022-11-30
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.
High-Dimensional Covariance Estimation
Author: Mohsen Pourahmadi
language: en
Publisher: John Wiley & Sons
Release Date: 2013-05-28
Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.