Author: Dietrich von Rosen
Publisher: Springer
ISBN: 3319787845
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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.
Author: Joseph Nzabanita
Publisher: Linköping University Electronic Press
ISBN: 9175190702
Category : Matrices
Languages : en
Pages : 51
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Book Description
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.
Author: Alvin C. Rencher
Publisher: John Wiley & Sons
ISBN: 0470192607
Category : Mathematics
Languages : en
Pages : 690
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Book Description
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
Author: Barry C. Arnold
Publisher: Springer Nature
ISBN: 3030836703
Category : Mathematics
Languages : en
Pages : 447
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Book Description
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!
Author: Igor Farkaš
Publisher: Springer Nature
ISBN: 3030616096
Category : Computers
Languages : en
Pages : 891
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Book Description
The proceedings set LNCS 12396 and 12397 constitute the proceedings of the 29th International Conference on Artificial Neural Networks, ICANN 2020, held in Bratislava, Slovakia, in September 2020.* The total of 139 full papers presented in these proceedings was carefully reviewed and selected from 249 submissions. They were organized in 2 volumes focusing on topics such as adversarial machine learning, bioinformatics and biosignal analysis, cognitive models, neural network theory and information theoretic learning, and robotics and neural models of perception and action. *The conference was postponed to 2021 due to the COVID-19 pandemic.
Author: R. Dennis Cook
Publisher: CRC Press
ISBN: 1040051324
Category : Mathematics
Languages : en
Pages : 448
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Book Description
Partial least squares (PLS) regression is, at its historical core, a black-box algorithmic method for dimension reduction and prediction based on an underlying linear relationship between a possibly vector-valued response and a number of predictors. Through envelopes, much more has been learned about PLS regression, resulting in a mass of information that allows an envelope bridge that takes PLS regression from a black-box algorithm to a core statistical paradigm based on objective function optimization and, more generally, connects the applied sciences and statistics in the context of PLS. This book focuses on developing this bridge. It also covers uses of PLS outside of linear regression, including discriminant analysis, non-linear regression, generalized linear models and dimension reduction generally. Key Features: • Showcases the first serviceable method for studying high-dimensional regressions. • Provides necessary background on PLS and its origin. • R and Python programs are available for nearly all methods discussed in the book. This book can be used as a reference and as a course supplement at the Master's level in Statistics and beyond. It will be of interest to both statisticians and applied scientists.
Author: Rudolf Freund
Publisher: John Wiley & Sons
ISBN: 0471416649
Category : Mathematics
Languages : en
Pages : 258
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Book Description
SAS® System for Regression Learn to perform a wide variety of regression analyses using SAS® software with this example-driven revised favorite from SAS Publishing. With this Third Edition you will learn the basics of performing regression analyses using a wide variety of models including nonlinear models. Other topics covered include performing linear regression analyses using PROC REG diagnosing and providing remedies for data problems, including outliers and multicollinearity. Examples feature numerous SAS procedures including REG, PLOT, GPLOT, NLIN, RSREG, AUTOREG, PRINCOMP, and others. A helpful discussion of theory is supplied where necessary. Some knowledge of both regression and the SAS System are assumed. New for this edition The Third Edition includes revisions, updated material, and new material. You’ll find new information on using SAS/INSIGHT® software regression with a binary response with emphasis on PROC LOGISTIC nonparametric regression (smoothing) using moving averages and PROC LOESS. Additionally, updated material throughout the book includes high-resolution PROC REG graphics output, using the OUTEST option to produce a data set, and using PROC SCORE to predict another data set.
Author: S. Selvin
Publisher: Cambridge University Press
ISBN: 1107113083
Category : Mathematics
Languages : en
Pages : 579
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Book Description
A Biostatistics Toolbox for Data Analysis delivers a sophisticated package of statistical methods for advanced master's (MPH) and PhD students in public health and epidemiology who are involved in the analysis of data. The book's statistical tools are organized into sections with similar objectives, each of which is accompanied by complete instructions, explanations, detailed examples, and advice on relevant issues and potential pitfalls.
Author: George Acquaah
Publisher: John Wiley & Sons
ISBN: 1119626692
Category : Science
Languages : en
Pages : 855
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Book Description
The revised edition of the bestselling textbook, covering both classical and molecular plant breeding Principles of Plant Genetics and Breeding integrates theory and practice to provide an insightful examination of the fundamental principles and advanced techniques of modern plant breeding. Combining both classical and molecular tools, this comprehensive textbook describes the multidisciplinary strategies used to produce new varieties of crops and plants, particularly in response to the increasing demands to of growing populations. Illustrated chapters cover a wide range of topics, including plant reproductive systems, germplasm for breeding, molecular breeding, the common objectives of plant breeders, marketing and societal issues, and more. Now in its third edition, this essential textbook contains extensively revised content that reflects recent advances and current practices. Substantial updates have been made to its molecular genetics and breeding sections, including discussions of new breeding techniques such as zinc finger nuclease, oligonucleotide directed mutagenesis, RNA-dependent DNA methylation, reverse breeding, genome editing, and others. A new table enables efficient comparison of an expanded list of molecular markers, including Allozyme, RFLPs, RAPD, SSR, ISSR, DAMD, AFLP, SNPs and ESTs. Also, new and updated “Industry Highlights” sections provide examples of the practical application of plant breeding methods to real-world problems. This new edition: Organizes topics to reflect the stages of an actual breeding project Incorporates the most recent technologies in the field, such as CRSPR genome edition and grafting on GM stock Includes numerous illustrations and end-of-chapter self-assessment questions, key references, suggested readings, and links to relevant websites Features a companion website containing additional artwork and instructor resources Principles of Plant Genetics and Breeding offers researchers and professionals an invaluable resource and remains the ideal textbook for advanced undergraduates and graduates in plant science, particularly those studying plant breeding, biotechnology, and genetics.
Author: Thomas Holgersson
Publisher: Springer Nature
ISBN: 3030567737
Category : Mathematics
Languages : en
Pages : 377
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Book Description
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.
