Multivariate data routinely collected nowadays using modern technological devices display cross-sectional, temporal, and spatial dependence. Regressions in Covariances, Dependencies and Graphs emphasizes the phenomenal roles of regression in modeling various dependencies using the twin principles of parsimony and regularization as a guide. For parsimony, covariance regression, mimicking the mean-regression, expresses a covariance matrix or its transform as linear combinations of covariates with the aim of reaching the versatility of the generalized linear models. Hidden regression reparametrizes a matrix so as to view its columns as parameters of certain regression models to be estimated iteratively one column at a time via regularized regression. The class of graphical Lasso algorithms for sparse graphs and their central roles in the modern high-dimensional data analysis are highlighted. Dimension-reduction through principal component analysis and factor models for multivariate and time series data is illustrated with a particular focus on the role of approximate factor models in the analysis of business and economics data.The methodologies are illustrated using genuine datasets. At the end of each chapter, practical, ready-to-run R scripts reinforce understanding and hands-on applications. A companion R package recode is specifically designed to complement the book's content, featuring real-world and simulated datasets along with a variety of functions to implement and visualize the concepts and results. The book, together with its accompanying R package, helps to bridge the gap between theory and practice, providing the tools one needs to apply advanced and some state-of-the-art statistical methods to real-world scenarios.Key Features: Promotes the regression idea as a unifying framework to model not just the means, but also covariance matrices, graphs and copulas using covariates. Highlights the implicit role of Cholesky factor in modeling various dependencies. Covers both undirected graphical models and directed graphs for modeling conditional independence structure. Bridges the gap between theory and methodology through data examples and exercises in each chapter. An R package (recode) containing datasets and implementation functions.
