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Author: Dietrich von Rosen
Publisher: Springer
ISBN: 3319787845
Category : Mathematics
Languages : en
Pages : 473
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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: Dietrich von Rosen
Publisher: Springer
ISBN: 3319787845
Category : Mathematics
Languages : en
Pages : 473
Get Book Here
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: Donald A. Burns
Publisher: CRC Press
ISBN: 9781420002577
Category : Science
Languages : en
Pages : 834
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Book Description
With contributions from over 40 experts in the field, this reference presents comprehensive, single-source coverage of the instrumentation, computerization, calibration, and methods development of NIR spectroscopy. It provides novel applications for accurate time- and cost-effective analyses of pharmaceuticals, polymers, textiles, agricultural products, dairy products, foods, and beverages. Emphasizing trends in sample preparation, the book covers historical development, calibration transfer, biomedical applications, plastics, and counterfeiting; on-line, in-line, and at-line analyses for process control, multilinear regression and principal component analysis, and more.
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: Donald A. Burns
Publisher: CRC Press
ISBN: 1420007378
Category : Science
Languages : en
Pages : 836
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Book Description
Fast, inexpensive, and easy-to-use, near-infrared (NIR) spectroscopy can be used to analyze small samples of virtually any composition. The Handbook of Near Infrared Analysis, Third Edition explains how to perform accurate as well as time- and cost-effective analyses across a growing spectrum of disciplines. Presenting nearly 50% new and re
Author: Daniel C. Harris
Publisher: Macmillan
ISBN: 9780716705710
Category : Science
Languages : en
Pages : 644
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Book Description
'Exploring Chemical Analysis' teaches students how to understand analytical results and how to use quantitative manipulations, preparing them for the problems they will encounter.
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: William D. Penny
Publisher: Elsevier
ISBN: 0080466508
Category : Psychology
Languages : en
Pages : 689
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Book Description
In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. - An essential reference and companion for users of the SPM software - Provides a complete description of the concepts and procedures entailed by the analysis of brain images - Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data - Stands as a compendium of all the advances in neuroimaging data analysis over the past decade - Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes - Structured treatment of data analysis issues that links different modalities and models - Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible
Author: Steve Selvin
Publisher: Cambridge University Press
ISBN: 1316473058
Category : Medical
Languages : en
Pages : 579
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Book Description
This sophisticated package of statistical methods is for advanced master's (MPH) and PhD students in public health and epidemiology who are involved in the analysis of data. It makes the link from statistical theory to data analysis, focusing on the methods and data types most common in public health and related fields. Like most toolboxes, the statistical tools in this book are organized into sections with similar objectives. Unlike most toolboxes, however, these tools are accompanied by complete instructions, explanations, detailed examples, and advice on relevant issues and potential pitfalls - conveying skills, intuition, and experience. The only prerequisite is a first-year statistics course and familiarity with a computing package such as R, Stata, SPSS, or SAS. Though the book is not tied to a particular computing language, its figures and analyses were all created using R. Relevant R code, data sets, and links to public data sets are available from www.cambridge.org/9781107113084.
Author: Kamal Karlapalem
Publisher: Springer Nature
ISBN: 3030757625
Category : Computers
Languages : en
Pages : 865
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Book Description
The 3-volume set LNAI 12712-12714 constitutes the proceedings of the 25th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining, PAKDD 2021, which was held during May 11-14, 2021. The 157 papers included in the proceedings were carefully reviewed and selected from a total of 628 submissions. They were organized in topical sections as follows: Part I: Applications of knowledge discovery and data mining of specialized data; Part II: Classical data mining; data mining theory and principles; recommender systems; and text analytics; Part III: Representation learning and embedding, and learning from data.
Author: Yong Shi
Publisher: Springer Science & Business Media
ISBN: 3642022987
Category : Computers
Languages : en
Pages : 871
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Book Description
MCDM 2009, the 20th International Conference on Multiple-Criteria Decision M- ing, emerged as a global forum dedicated to the sharing of original research results and practical development experiences among researchers and application developers from different multiple-criteria decision making-related areas such as multiple-criteria decision aiding, multiple criteria classification, ranking, and sorting, multiple obj- tive continuous and combinatorial optimization, multiple objective metaheuristics, multiple-criteria decision making and preference modeling, and fuzzy multiple-criteria decision making. The theme for MCDM 2009 was “New State of MCDM in the 21st Century.” The conference seeks solutions to challenging problems facing the development of multiple-criteria decision making, and shapes future directions of research by prom- ing high-quality, novel and daring research findings. With the MCDM conference, these new challenges and tools can easily be shared with the multiple-criteria decision making community. The workshop program included nine workshops which focused on different topics in new research challenges and initiatives of MCDM. We received more than 350 submissions for all the workshops, out of which 121 were accepted. This includes 72 regular papers and 49 short papers. We would like to thank all workshop organizers and the Program Committee for the excellent work in maintaining the conference’s standing for high-quality papers.
