High Dimensional Covariance Estimation

Author: Mohsen Pourahmadi
Publisher: John Wiley & Sons
ISBN: 1118034295
Format: PDF, Kindle
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"Focusing on methodology and computation more than on theorems and proofs, this book provides computationally feasible and statistically efficient methods for estimating sparse and large covariance matrices of high-dimensional data. Extensive in breadth and scope, it features ample applications to a number of applied areas, including business and economics, computer science, engineering, and financial mathematics; recognizes the important and significant contributions of longitudinal and spatial data; and includes various computer codes in R throughout the text and on an author-maintained web site"--

Multivariate Statistics

Author: Yasunori Fujikoshi
Publisher: John Wiley & Sons
ISBN: 0470539860
Format: PDF, Docs
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A comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic tools and exact distributional results of multivariate statistics, and, in addition, the derivations of most distributional results are provided. Statistical methods for high-dimensional data, such as curve data, spectra, images, and DNA microarrays, are discussed. Bootstrap approximations from a methodological point of view, theoretical accuracies in MANOVA tests, and model selection criteria are also presented. Subsequent chapters feature additional topical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance in discriminant analysis, growth curve models, generalized linear models, profile analysis, and multiple comparison Each chapter provides real-world applications and thorough analyses of the real data. In addition, approximation formulas found throughout the book are a useful tool for both practical and theoretical statisticians, and basic results on exact distributions in multivariate analysis are included in a comprehensive, yet accessible, format. Multivariate Statistics is an excellent book for courses on probability theory in statistics at the graduate level. It is also an essential reference for both practical and theoretical statisticians who are interested in multivariate analysis and who would benefit from learning the applications of analytical probabilistic methods in statistics.

Smart Grid using Big Data Analytics

Author: Robert C. Qiu
Publisher: John Wiley & Sons
ISBN: 1118716809
Format: PDF, Docs
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This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.

High Dimensional Probability

Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Format: PDF, ePub
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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Linear Models and Time Series Analysis

Author: Marc S. Paolella
Publisher: John Wiley & Sons
ISBN: 1119431859
Format: PDF, Docs
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A comprehensive and timely edition on an emerging new trend in time series Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH sets a strong foundation, in terms of distribution theory, for the linear model (regression and ANOVA), univariate time series analysis (ARMAX and GARCH), and some multivariate models associated primarily with modeling financial asset returns (copula-based structures and the discrete mixed normal and Laplace). It builds on the author's previous book, Fundamental Statistical Inference: A Computational Approach, which introduced the major concepts of statistical inference. Attention is explicitly paid to application and numeric computation, with examples of Matlab code throughout. The code offers a framework for discussion and illustration of numerics, and shows the mapping from theory to computation. The topic of time series analysis is on firm footing, with numerous textbooks and research journals dedicated to it. With respect to the subject/technology, many chapters in Linear Models and Time-Series Analysis cover firmly entrenched topics (regression and ARMA). Several others are dedicated to very modern methods, as used in empirical finance, asset pricing, risk management, and portfolio optimization, in order to address the severe change in performance of many pension funds, and changes in how fund managers work. Covers traditional time series analysis with new guidelines Provides access to cutting edge topics that are at the forefront of financial econometrics and industry Includes latest developments and topics such as financial returns data, notably also in a multivariate context Written by a leading expert in time series analysis Extensively classroom tested Includes a tutorial on SAS Supplemented with a companion website containing numerous Matlab programs Solutions to most exercises are provided in the book Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH is suitable for advanced masters students in statistics and quantitative finance, as well as doctoral students in economics and finance. It is also useful for quantitative financial practitioners in large financial institutions and smaller finance outlets.

Foundations of Time Series Analysis and Prediction Theory

Author: Mohsen Pourahmadi
Publisher: John Wiley & Sons
ISBN: 9780471394341
Format: PDF, Docs
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Foundations of time series for researchers and students This volume provides a mathematical foundation for time series analysis and prediction theory using the idea of regression and the geometry of Hilbert spaces. It presents an overview of the tools of time series data analysis, a detailed structural analysis of stationary processes through various reparameterizations employing techniques from prediction theory, digital signal processing, and linear algebra. The author emphasizes the foundation and structure of time series and backs up this coverage with theory and application. End-of-chapter exercises provide reinforcement for self-study and appendices covering multivariate distributions and Bayesian forecasting add useful reference material. Further coverage features: * Similarities between time series analysis and longitudinal data analysis * Parsimonious modeling of covariance matrices through ARMA-like models * Fundamental roles of the Wold decomposition and orthogonalization * Applications in digital signal processing and Kalman filtering * Review of functional and harmonic analysis and prediction theory Foundations of Time Series Analysis and Prediction Theory guides readers from the very applied principles of time series analysis through the most theoretical underpinnings of prediction theory. It provides a firm foundation for a widely applicable subject for students, researchers, and professionals in diverse scientific fields.

Probabilistic Graphical Models for Genetics Genomics and Postgenomics

Author: Raphaël Mourad
Publisher: OUP Oxford
ISBN: 0191019208
Format: PDF, ePub, Docs
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Nowadays bioinformaticians and geneticists are faced with myriad high-throughput data usually presenting the characteristics of uncertainty, high dimensionality and large complexity. These data will only allow insights into this wealth of so-called 'omics' data if represented by flexible and scalable models, prior to any further analysis. At the interface between statistics and machine learning, probabilistic graphical models (PGMs) represent a powerful formalism to discover complex networks of relations. These models are also amenable to incorporating a priori biological information. Network reconstruction from gene expression data represents perhaps the most emblematic area of research where PGMs have been successfully applied. However these models have also created renewed interest in genetics in the broad sense, in particular regarding association genetics, causality discovery, prediction of outcomes, detection of copy number variations, and epigenetics. This book provides an overview of the applications of PGMs to genetics, genomics and postgenomics to meet this increased interest. A salient feature of bioinformatics, interdisciplinarity, reaches its limit when an intricate cooperation between domain specialists is requested. Currently, few people are specialists in the design of advanced methods using probabilistic graphical models for postgenomics or genetics. This book deciphers such models so that their perceived difficulty no longer hinders their use and focuses on fifteen illustrations showing the mechanisms behind the models. Probabilistic Graphical Models for Genetics, Genomics and Postgenomics covers six main themes: (1) Gene network inference (2) Causality discovery (3) Association genetics (4) Epigenetics (5) Detection of copy number variations (6) Prediction of outcomes from high-dimensional genomic data. Written by leading international experts, this is a collection of the most advanced work at the crossroads of probabilistic graphical models and genetics, genomics, and postgenomics. The self-contained chapters provide an enlightened account of the pros and cons of applying these powerful techniques.

Applied Linear Regression

Author: Sanford Weisberg
Publisher: John Wiley & Sons
ISBN: 1118594851
Format: PDF
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Praise for the Third Edition "...this is an excellent book which could easily be used as a course text..." —International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illustrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. While maintaining the accessible appeal of each previous edition,Applied Linear Regression, Fourth Edition features: Graphical methods stressed in the initial exploratory phase, analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple and complex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, and variance assumptions Updated methodology, such as bootstrapping, cross-validation binomial and Poisson regression, and modern model selection methods Applied Linear Regression, Fourth Edition is an excellent textbook for upper-undergraduate and graduate-level students, as well as an appropriate reference guide for practitioners and applied statisticians in engineering, business administration, economics, and the social sciences.