Large Covariance And Autocovariance Matrices
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Large Covariance And Autocovariance Matrices
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Author : Arup Bose
language : en
Publisher: CRC Press
Release Date : 2018-07-03
Large Covariance And Autocovariance Matrices written by Arup Bose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Mathematics categories.
Estimation of large dispersion and autocovariance matrices using banding and tapering Joint convergence of high dimensional generalized dispersion matrices Limiting spectral distribution of symmetric polynomials in sample autocovariance matrices and normality of traces Application of free probability in high dimensional time series Estimation of coefficient matrices in high dimensional autoregressive process
Probability And Stochastic Processes
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Author : Siva Athreya
language : en
Publisher: Springer Nature
Release Date : 2024-08-03
Probability And Stochastic Processes written by Siva Athreya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-03 with Mathematics categories.
The book collects papers on several topics in probability and stochastic processes. These papers have been presented at a conference organised in honour of Professor Rajeeva L. Karandikar who turned 65 in 2021. He was a distinguished researcher and a teacher at the Indian Statistical Institute (ISI), Delhi Centre, for many years. He has been a multi-faceted academician, interacting with the Government of India and the industry. He has left an indelible mark in every endeavour of his and in his several different avatars—be it in the ISI, in the industry or as Director of Chennai Mathematical Institute. This book will be useful to senior undergraduate and graduate students, as well as researchers in probability, statistics and related fields.
High Dimensional Covariance Estimation
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Author : Mohsen Pourahmadi
language : en
Publisher: John Wiley & Sons
Release Date : 2013-05-28
High Dimensional Covariance Estimation written by Mohsen Pourahmadi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-28 with Mathematics categories.
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.
Random Matrices And Non Commutative Probability
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Author : Arup Bose
language : en
Publisher: CRC Press
Release Date : 2021-10-26
Random Matrices And Non Commutative Probability written by Arup Bose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-26 with Mathematics categories.
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Random Circulant Matrices
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Author : Arup Bose
language : en
Publisher: CRC Press
Release Date : 2018-11-05
Random Circulant Matrices written by Arup Bose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
Sparse Graphical Modeling For High Dimensional Data
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Author : Faming Liang
language : en
Publisher: CRC Press
Release Date : 2023-08-02
Sparse Graphical Modeling For High Dimensional Data written by Faming Liang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-02 with Mathematics categories.
This book provides a general framework for learning sparse graphical models with conditional independence tests. It includes complete treatments for Gaussian, Poisson, multinomial, and mixed data; unified treatments for covariate adjustments, data integration, and network comparison; unified treatments for missing data and heterogeneous data; efficient methods for joint estimation of multiple graphical models; effective methods of high-dimensional variable selection; and effective methods of high-dimensional inference. The methods possess an embarrassingly parallel structure in performing conditional independence tests, and the computation can be significantly accelerated by running in parallel on a multi-core computer or a parallel architecture. This book is intended to serve researchers and scientists interested in high-dimensional statistics, and graduate students in broad data science disciplines. Key Features: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference
Introduction To High Dimensional Statistics
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Author : Christophe Giraud
language : en
Publisher: CRC Press
Release Date : 2021-08-25
Introduction To High Dimensional Statistics written by Christophe Giraud and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-25 with Business & Economics categories.
Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
U Statistics Mm Estimators And Resampling
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Author : Arup Bose
language : en
Publisher: Springer
Release Date : 2018-08-28
U Statistics Mm Estimators And Resampling written by Arup Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.
This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U-statistics and Mm-estimators and develops their asymptotic properties. It also provides an elementary introduction to resampling, particularly in the context of these estimators. The last chapter is on practical implementation of the methods presented in other chapters, using the free software R.
Time Series Analysis Methods And Applications
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Author :
language : en
Publisher: Elsevier
Release Date : 2012-05-18
Time Series Analysis Methods And Applications written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-18 with Mathematics categories.
The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments.The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. - Comprehensively presents the various aspects of statistical methodology - Discusses a wide variety of diverse applications and recent developments - Contributors are internationally renowened experts in their respective areas
Cognitive Radio Communication And Networking
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Author : Robert Caiming Qiu
language : en
Publisher: John Wiley & Sons
Release Date : 2012-09-10
Cognitive Radio Communication And Networking written by Robert Caiming Qiu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-10 with Technology & Engineering categories.
The author presents a unified treatment of this highly interdisciplinary topic to help define the notion of cognitive radio. The book begins with addressing issues such as the fundamental system concept and basic mathematical tools such as spectrum sensing and machine learning, before moving on to more advanced concepts and discussions about the future of cognitive radio. From the fundamentals in spectrum sensing to the applications of cognitive algorithms to radio communications, and discussion of radio platforms and testbeds to show the applicability of the theory to practice, the author aims to provide an introduction to a fast moving topic for students and researchers seeking to develop a thorough understanding of cognitive radio networks. Examines basic mathematical tools before moving on to more advanced concepts and discussions about the future of cognitive radio Describe the fundamentals of cognitive radio, providing a step by step treatment of the topics to enable progressive learning Includes questions, exercises and suggestions for extra reading at the end of each chapter Topics covered in the book include: Spectrum Sensing: Basic Techniques; Cooperative Spectrum Sensing Wideband Spectrum Sensing; Agile Transmission Techniques: Orthogonal Frequency Division Multiplexing Multiple Input Multiple Output for Cognitive Radio; Convex Optimization for Cognitive Radio; Cognitive Core (I): Algorithms for Reasoning and Learning; Cognitive Core (II): Game Theory; Cognitive Radio Network IEEE 802.22: The First Cognitive Radio Wireless Regional Area Network Standard, and Radio Platforms and Testbeds.