Bilinear Regression Analysis

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. Front Matter ....Pages i-xiii Introduction (Dietrich von Rosen)....Pages 1-37 The Basic Ideas of Obtaining MLEs: A Known Dispersion (Dietrich von Rosen)....Pages 39-70 The Basic Ideas of Obtaining MLEs: Unknown Dispersion (Dietrich von Rosen)....Pages 71-97 Basic Properties of Estimators (Dietrich von Rosen)....Pages 99-175 Density Approximations (Dietrich von Rosen)....Pages 177-220 Residuals (Dietrich von Rosen)....Pages 221-280 Testing Hypotheses (Dietrich von Rosen)....Pages 281-361 Influential Observations (Dietrich von Rosen)....Pages 363-421 Back Matter ....Pages 423-468