Mohsen Pourahmadi – författare

Foundations of time series for researchers and students This volume provides a mathematical foundation for time seriesanalysis and prediction theory using the idea of regression and thegeometry of Hilbert spaces. It presents an overview of the tools oftime series data analysis, a detailed structural analysis ofstationary processes through various reparameterizations employingtechniques from prediction theory, digital signal processing, andlinear algebra. The author emphasizes the foundation and structureof time series and backs up this coverage with theory andapplication. End-of-chapter exercises provide reinforcement for self-study andappendices covering multivariate distributions and Bayesianforecasting add useful reference material. Further coveragefeatures:* Similarities between time series analysis and longitudinal dataanalysis* Parsimonious modeling of covariance matrices through ARMA-likemodels* Fundamental roles of the Wold decomposition andorthogonalization* Applications in digital signal processing and Kalmanfiltering* Review of functional and harmonic analysis and predictiontheory Foundations of Time Series Analysis and Prediction Theory guidesreaders from the very applied principles of time series analysisthrough the most theoretical underpinnings of prediction theory. Itprovides a firm foundation for a widely applicable subject forstudents, researchers, and professionals in diverse scientificfields.

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.

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.

Methods for estimating sparse and large covariance matricesCovariance 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 RegularizationRegularizing the EigenstructureBanding, Tapering, and ThresholdingCovariance MatricesSparse Gaussian Graphical ModelsMultivariate RegressionThe 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.

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.