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.

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.

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.

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.

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.

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.

Engineering geologists face the task of addressing geological factors that can affect planning with little time and with few resources. A solution is using the right tools to save time searching for answers and devote attention to making critical engineering decisions. The Handbook of Research on Trends and Digital Advances in Engineering Geology is an essential reference source for the latest research on new trends, technology, and computational methods that can model engineering phenomena automatically. Featuring exhaustive coverage on a broad range of topics and perspectives such as acoustic energy, landslide mapping, and natural hazards, this publication is ideally designed for academic scientists, industry and applied researchers, and policy and decision makers seeking current research on new tools to aid in timely decision-making of critical engineering situations.

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

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.

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!