Von Rosen D. Bilinear Regression Analysis. An Introduction 2018

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Von Rosen D. Bilinear Regression Analysis. An Introduction 2018

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Textbook in PDF format 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. Front Matter Introduction The Basic Ideas of Obtaining MLEs: A Known Dispersion The Basic Ideas of Obtaining MLEs: Unknown Dispersion Basic Properties of Estimators Density Approximations Residuals Testing Hypotheses Influential Observations Back Matter