Bilinear Regression Analysis
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Bilinear Regression Analysis
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Author : Dietrich Von Rosen
language : en
Publisher:
Release Date : 2018
Bilinear Regression Analysis written by Dietrich Von Rosen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Algebra categories.
This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph. D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.
Bilinear And Trilinear Regression Models With Structured Covariance Matrices
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Author : Joseph Nzabanita
language : en
Publisher: Linköping University Electronic Press
Release Date : 2015-05-21
Bilinear And Trilinear Regression Models With Structured Covariance Matrices written by Joseph Nzabanita and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-21 with Matrices categories.
This thesis focuses on the problem of estimating parameters in bilinear and trilinear regression models in which random errors are normally distributed. In these models the covariance matrix has a Kronecker product structure and some factor matrices may be linearly structured. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model’s estimated mean parameters. Firstly, the extended growth curve model with a linearly structured covariance matrix is considered. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into appropriate orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied. Secondly, we study a bilinear regression model with matrix normally distributed random errors. For those models, the dispersion matrix follows a Kronecker product structure and it can be used, for example, to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations, a flip-flop relation, are established. At last, the models based on normally distributed random third order tensors are studied. These models are useful in analyzing 3-dimensional data arrays. In some studies the analysis is done using the tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker structure. Little attention is paid to the structure of the mean, however, there is a potential to improve the analysis by assuming a structured mean. We formally introduce a 2-fold growth curve model by assuming a trilinear structure for the mean in the tensor normal model and propose an estimation algorithm for parameters. Also some extensions are discussed.
Bilinear Regression Analysis
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Author : Dietrich von Rosen
language : en
Publisher: Springer
Release Date : 2018-08-02
Bilinear Regression Analysis written by Dietrich von Rosen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Mathematics categories.
This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph.D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.
Linear Regression Analysis
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Author : Xin Yan
language : en
Publisher: World Scientific
Release Date : 2009
Linear Regression Analysis written by Xin Yan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
"This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.
Introduction To Regression Analysis
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Author : Michael A. Golberg
language : en
Publisher: WIT Press
Release Date : 2004
Introduction To Regression Analysis written by Michael A. Golberg and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
In order to apply regression analysis effectively, it is necessary to understand both the underlying theory and its practical application. This book explores conventional topics as well as recent practical developments, linking theory with application. Intended to continue from where most basic statistics texts end, it is designed primarily for advanced undergraduates, graduate students and researchers in various fields of engineering, chemical and physical sciences, mathematical sciences and statistics.
Regression Analysis
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Author : Ashish Sen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Regression Analysis written by Ashish Sen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Psychology categories.
An up-to-date, rigorous, and lucid treatment of the theory, methods, and applications of regression analysis, and thus ideally suited for those interested in the theory as well as those whose interests lie primarily with applications. It is further enhanced through real-life examples drawn from many disciplines, showing the difficulties typically encountered in the practice of regression analysis. Consequently, this book provides a sound foundation in the theory of this important subject.
Linear Regression Analysis With Jmp And R
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Author : Rachel T. Silvestrini
language : en
Publisher: Quality Press
Release Date : 2018-04-26
Linear Regression Analysis With Jmp And R written by Rachel T. Silvestrini and has been published by Quality Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Education categories.
This comprehensive but low-cost textbook is intended for use in an undergraduate level regression course, as well as for use by practitioners. The authors have included some statistical details throughout the book but focus on interpreting results for real applications of regression analysis. Chapters are devoted to data collection and cleaning; data visualization; model fitting and inference; model prediction and inference; model diagnostics; remedial measures; model selection techniques; model validation; and a case study demonstrating the techniques outlined throughout the book. The examples throughout each chapter are illustrated using the software packages R and JMP. At the end of each chapter, there is a tutorial section demonstrating the use of both R and JMP. The R tutorial contains source code and the JMP tutorial contains a step by step guide. Each chapter also includes exercises for further study and learning.
A Modification Of The Least Squares Join Point Estimator In Bilinear Segmented Regression
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Author : Walter W. Piegorsch
language : en
Publisher:
Release Date : 1982
A Modification Of The Least Squares Join Point Estimator In Bilinear Segmented Regression written by Walter W. Piegorsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Least squares categories.
Handbook Of Regression Analysis
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Author : Samprit Chatterjee
language : en
Publisher: John Wiley & Sons
Release Date : 2013-05-30
Handbook Of Regression Analysis written by Samprit Chatterjee 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 2013-05-30 with Mathematics categories.
A Comprehensive Account for Data Analysts of the Methods and Applications of Regression Analysis. Written by two established experts in the field, the purpose of the Handbook of Regression Analysis is to provide a practical, one-stop reference on regression analysis. The focus is on the tools that both practitioners and researchers use in real life. It is intended to be a comprehensive collection of the theory, methods, and applications of regression methods, but it has been deliberately written at an accessible level. The handbook provides a quick and convenient reference or “refresher” on ideas and methods that are useful for the effective analysis of data and its resulting interpretations. Students can use the book as an introduction to and/or summary of key concepts in regression and related course work (including linear, binary logistic, multinomial logistic, count, and nonlinear regression models). Theory underlying the methodology is presented when it advances conceptual understanding and is always supplemented by hands-on examples. References are supplied for readers wanting more detailed material on the topics discussed in the book. R code and data for all of the analyses described in the book are available via an author-maintained website. "I enjoyed the presentation of the Handbook, and I would be happy to recommend this nice handy book as a reference to my students. The clarity of the writing and proper choices of examples allows the presentations ofmany statisticalmethods shine. The quality of the examples at the end of each chapter is a strength. They entail explanations of the resulting R outputs and successfully guide readers to interpret them." American Statistician
Contemporary Experimental Design Multivariate Analysis And Data Mining
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Author : Jianqing Fan
language : en
Publisher: Springer Nature
Release Date : 2020-05-22
Contemporary Experimental Design Multivariate Analysis And Data Mining written by Jianqing Fan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-22 with Mathematics categories.
The collection and analysis of data play an important role in many fields of science and technology, such as computational biology, quantitative finance, information engineering, machine learning, neuroscience, medicine, and the social sciences. Especially in the era of big data, researchers can easily collect data characterised by massive dimensions and complexity. In celebration of Professor Kai-Tai Fang’s 80th birthday, we present this book, which furthers new and exciting developments in modern statistical theories, methods and applications. The book features four review papers on Professor Fang’s numerous contributions to the fields of experimental design, multivariate analysis, data mining and education. It also contains twenty research articles contributed by prominent and active figures in their fields. The articles cover a wide range of important topics such as experimental design, multivariate analysis, data mining, hypothesis testing and statistical models.