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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.
List of contents
Preface.- 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.- Appendices.- Indices.
About the author
Dietrich von Rosen is a professor at the Department of Energy and Technology at the Swedish University of Agricultural Sciences. He graduated in mathematical statistics from Stockholm University, Sweden. His main research interest is multivariate analysis and its extensions, including repeated measurements analysis and high-dimensional analysis. He has published more than 100 papers, the majority of which are within the above areas, as well as a book on advanced multivariate statistics and matrices in collaboration with Tõnu Kollo, professor of mathematical statistics at the University of Tartu, Estonia.
Summary
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.
Additional text
“It is an interesting book, strongly recommended to researchers who have an interest in the topic of bilinear regression.” (Michel H. Montoril, Mathematical Reviews, August, 2019)
“The present book offers a complete presentation of the statistical techniques concerning bilinear regression analysis. … A special mention goes to the bibliography that accompanies each chapter. Far from being a simple list of papers containing the results recalled in the text, it is a real history of statistics, where the early ideas of bilinear regression are highlighted.” (Fabio Rapallo, zbMATH 1398.62003, 2018)
Report
"It is an interesting book, strongly recommended to researchers who have an interest in the topic of bilinear regression." (Michel H. Montoril, Mathematical Reviews, August, 2019)
"The present book offers a complete presentation of the statistical techniques concerning bilinear regression analysis. ... A special mention goes to the bibliography that accompanies each chapter. Far from being a simple list of papers containing the results recalled in the text, it is a real history of statistics, where the early ideas of bilinear regression are highlighted." (Fabio Rapallo, zbMATH 1398.62003, 2018)
