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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.

Regression analysis. --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Mathematical statistics. --- Matrix theory. --- Statistics. --- Statistical Theory and Methods. --- Linear and Multilinear Algebras, Matrix Theory. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics . --- Algebra. --- Mathematical analysis

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This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference. .

Linear models (Statistics) --- Mathematical statistics --- Statistics. --- Statistical Theory and Methods. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Statistics and Computing/Statistics Programs. --- Models, Linear (Statistics) --- Mathematical models --- Statistics --- Mathematical statistics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistics . --- Biometry. --- Statistics in Business, Management, Economics, Finance, Insurance. --- Biostatistics. --- Statistics and Computing. --- Data processing. --- Biological statistics --- Biology --- Biometrics (Biology) --- Biostatistics --- Biomathematics

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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. .

Statistical science --- Algebra --- Mathematical statistics --- algebra --- lineaire algebra --- statistiek --- statistisch onderzoek

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