Recent Developments in Multivariate and Random Matrix Analysis

Recent Developments in Multivariate and Random Matrix Analysis

Author: Thomas Holgersson

Publisher: Springer Nature

Published: 2020-09-17

Total Pages: 377

ISBN-13: 3030567737

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This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as high-dimensional analysis, goodness-of-fit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.


Book Synopsis Recent Developments in Multivariate and Random Matrix Analysis by : Thomas Holgersson

Download or read book Recent Developments in Multivariate and Random Matrix Analysis written by Thomas Holgersson and published by Springer Nature. This book was released on 2020-09-17 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as high-dimensional analysis, goodness-of-fit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.

Multivariate, Multilinear and Mixed Linear Models

Multivariate, Multilinear and Mixed Linear Models

Author: Katarzyna Filipiak

Publisher: Springer Nature

Published: 2021-10-01

Total Pages: 357

ISBN-13: 3030754944

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This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Będlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.


Book Synopsis Multivariate, Multilinear and Mixed Linear Models by : Katarzyna Filipiak

Download or read book Multivariate, Multilinear and Mixed Linear Models written by Katarzyna Filipiak and published by Springer Nature. This book was released on 2021-10-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Będlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.

A Dynamical Approach to Random Matrix Theory

A Dynamical Approach to Random Matrix Theory

Author: László Erdős

Publisher: American Mathematical Soc.

Published: 2017-08-30

Total Pages: 226

ISBN-13: 1470436485

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A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.


Book Synopsis A Dynamical Approach to Random Matrix Theory by : László Erdős

Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Methodology and Applications of Statistics

Methodology and Applications of Statistics

Author: Barry C. Arnold

Publisher: Springer Nature

Published: 2022-01-04

Total Pages: 447

ISBN-13: 3030836703

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Dedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!


Book Synopsis Methodology and Applications of Statistics by : Barry C. Arnold

Download or read book Methodology and Applications of Statistics written by Barry C. Arnold and published by Springer Nature. This book was released on 2022-01-04 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!

Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications

Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications

Author: Zhidong Bai

Publisher: World Scientific

Published: 2009-07-27

Total Pages: 176

ISBN-13: 9814467995

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Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.


Book Synopsis Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications by : Zhidong Bai

Download or read book Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications written by Zhidong Bai and published by World Scientific. This book was released on 2009-07-27 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.

Advances in Guidance, Navigation and Control

Advances in Guidance, Navigation and Control

Author: Liang Yan

Publisher: Springer Nature

Published: 2023-02-10

Total Pages: 7455

ISBN-13: 9811966133

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This book features the latest theoretical results and techniques in the field of guidance, navigation, and control (GNC) of vehicles and aircrafts. It covers a wide range of topics, including but not limited to, intelligent computing communication and control; new methods of navigation, estimation and tracking; control of multiple moving objects; manned and autonomous unmanned systems; guidance, navigation and control of miniature aircraft; and sensor systems for guidance, navigation and control etc. Presenting recent advances in the form of illustrations, tables, and text, it also provides detailed information of a number of the studies, to offer readers insights for their own research. In addition, the book addresses fundamental concepts and studies in the development of GNC, making it a valuable resource for both beginners and researchers wanting to further their understanding of guidance, navigation, and control.


Book Synopsis Advances in Guidance, Navigation and Control by : Liang Yan

Download or read book Advances in Guidance, Navigation and Control written by Liang Yan and published by Springer Nature. This book was released on 2023-02-10 with total page 7455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features the latest theoretical results and techniques in the field of guidance, navigation, and control (GNC) of vehicles and aircrafts. It covers a wide range of topics, including but not limited to, intelligent computing communication and control; new methods of navigation, estimation and tracking; control of multiple moving objects; manned and autonomous unmanned systems; guidance, navigation and control of miniature aircraft; and sensor systems for guidance, navigation and control etc. Presenting recent advances in the form of illustrations, tables, and text, it also provides detailed information of a number of the studies, to offer readers insights for their own research. In addition, the book addresses fundamental concepts and studies in the development of GNC, making it a valuable resource for both beginners and researchers wanting to further their understanding of guidance, navigation, and control.

High-Dimensional Covariance Matrix Estimation

High-Dimensional Covariance Matrix Estimation

Author: Aygul Zagidullina

Publisher: Springer Nature

Published: 2021-10-29

Total Pages: 123

ISBN-13: 3030800652

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This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.


Book Synopsis High-Dimensional Covariance Matrix Estimation by : Aygul Zagidullina

Download or read book High-Dimensional Covariance Matrix Estimation written by Aygul Zagidullina and published by Springer Nature. This book was released on 2021-10-29 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.

Matrix Variate Distributions

Matrix Variate Distributions

Author: A K Gupta

Publisher: CRC Press

Published: 2018-05-02

Total Pages: 151

ISBN-13: 1351433008

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Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results. After a review of the essential background material, the authors investigate the range of matrix variate distributions, including: matrix variate normal distribution Wishart distribution Matrix variate t-distribution Matrix variate beta distribution F-distribution Matrix variate Dirichlet distribution Matrix quadratic forms With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.


Book Synopsis Matrix Variate Distributions by : A K Gupta

Download or read book Matrix Variate Distributions written by A K Gupta and published by CRC Press. This book was released on 2018-05-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results. After a review of the essential background material, the authors investigate the range of matrix variate distributions, including: matrix variate normal distribution Wishart distribution Matrix variate t-distribution Matrix variate beta distribution F-distribution Matrix variate Dirichlet distribution Matrix quadratic forms With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

Developments in Statistics

Developments in Statistics

Author: Paruchuri R. Krishnaiah

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 352

ISBN-13: 1483264866

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Development in Statistics, Volume 1 is a collection of papers that deals with theory and application of parameter estimation in stochastic differential systems, the comparative aspects of the study of ordinary time series, and real multivariate distributions. Some papers discuss covariance analysis of nonstationary time series, nonparametric repeated significance tests, as well as discrete optimal factorial designs for statisticians and investigators of experiments. One paper cites an application of parameter estimation in stochastic differential systems in approximates of stability and control derivatives from flight test data. Another paper cites cases where procedures of ordinary time series (or point processes) have direct analogs in the study of point processes (or ordinary time series). One paper explains the applications of multivariate distributions in simultaneous tests on the equality of eigenvalues toward the covariance matrix, canonical correlation matrix, and a matrix associated with the multivariate analysis of variance. Another paper reviews two types of repeated significance tests, namely, the genuinely distribution-free tests based on a broad class of nonparametric statistics; and the asymptotically distribution-free tests based on a broad class of parametric statistics but having asymptotically nonparametric behavior. Both types can provide a unified solution to a broad class of problems. The collection can be valuable for mathematicians, students, and professors of calculus, statistics, or advanced mathematics.


Book Synopsis Developments in Statistics by : Paruchuri R. Krishnaiah

Download or read book Developments in Statistics written by Paruchuri R. Krishnaiah and published by Academic Press. This book was released on 2014-06-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Development in Statistics, Volume 1 is a collection of papers that deals with theory and application of parameter estimation in stochastic differential systems, the comparative aspects of the study of ordinary time series, and real multivariate distributions. Some papers discuss covariance analysis of nonstationary time series, nonparametric repeated significance tests, as well as discrete optimal factorial designs for statisticians and investigators of experiments. One paper cites an application of parameter estimation in stochastic differential systems in approximates of stability and control derivatives from flight test data. Another paper cites cases where procedures of ordinary time series (or point processes) have direct analogs in the study of point processes (or ordinary time series). One paper explains the applications of multivariate distributions in simultaneous tests on the equality of eigenvalues toward the covariance matrix, canonical correlation matrix, and a matrix associated with the multivariate analysis of variance. Another paper reviews two types of repeated significance tests, namely, the genuinely distribution-free tests based on a broad class of nonparametric statistics; and the asymptotically distribution-free tests based on a broad class of parametric statistics but having asymptotically nonparametric behavior. Both types can provide a unified solution to a broad class of problems. The collection can be valuable for mathematicians, students, and professors of calculus, statistics, or advanced mathematics.

Advances in Multivariate Statistical Analysis

Advances in Multivariate Statistical Analysis

Author: Arjun K. Gupta

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 392

ISBN-13: 9401706530

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The death of Professor K.C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog nition of his many contributions in multivariate statis tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T.C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J.D. Knoke, W.J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D.K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.


Book Synopsis Advances in Multivariate Statistical Analysis by : Arjun K. Gupta

Download or read book Advances in Multivariate Statistical Analysis written by Arjun K. Gupta and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The death of Professor K.C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog nition of his many contributions in multivariate statis tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T.C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J.D. Knoke, W.J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D.K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.