Bilinear regression analysis. An introduction
The present book offers a complete presentation of the statistical techniques concerning bilinear regression analysis. After a brief introductory chapter where the main models of bilinear regression analysis are defined, the text proceeds with a detailed discussion of the classical topics related to the statistical models of this kind: maximum likelihood estimation of the parameters; properties of the estimators; analysis of the residuals; statistical tests for model selection; analysis of the influential observations. The style of the presentation is the style of a classic book in mathematical statistics, designed as a textbook for a PhD course. So, the presentation is generally essential, focused on technical aspects, and with few examples based on real data. Some details of the proofs are left to the reader, in the form of exercises. In any case, solid bases in linear algebra are necessary to fully understand the content of the book. 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. The reader will appreciate that some basic ideas now encompassed in the formalism of bilinear regression can be found in papers going back to the first half of the 20th century.
scientific article; zbMATH DE number 6919665