Professor Haruo Yanai and multivariate analysis

摘要

The late Professor Yanai has contributed to many fields ranging from aptitude diagnostics, epidemiology,and nursing to psychometrics and statistics. This paper reviews some of his accomplishments in multivariateanalysis through his collaborative work with the present author, along with some untold episodesfor the inception of key ideas underlying the work. The various topics covered include constrained principalcomponent analysis, extensions of Khatri’s lemma, theWedderburn-Guttman theorem, ridge operators, generalizedconstrained canonical correlation analysis, and causal inference. A common thread running throughall of them is projectors and singular value decomposition, which are the main subject matters of a recentmonograph by Yanai, Takeuchi, and Takane [60].