Some extremal properties of the singular values of a compact operator and their application to the factor analysis of a probability or a random function. II: Linear factor analysis criteria for a probability or a random function. (Quelques propriétés extrémales des valeurs singulières d’un opérateur compact et leurs applications aux analyses factorielles d’une probabilité ou d’une fonction aléatoire. II: Critères d’analyses factorielles linéaires d’une probabilité ou d’une fonction aléatoire.) (French) Zbl 1064.47507
Summary: This paper extends the work by C. Radhakrishna Rao [Sankhyā, Ser. A 26, 329–358 (1964; Zbl 0137.37207)] concerning factor analysis criteria equivalent to the principal component analysis of a finite set of random variables. We search for global (i.e., non-iterative) criteria for the factor analysis of a probability defined on a separable Hilbert space or of a real random function other than a finite or countable set of real random variables. We compare this analysis with principal component analysis defined in a general probabilistic setting by J. Dauxois and A. Pousse [Les analyses factorielles en calcul des probabilités et en statistique: Essai d’étude synthétique, Thèse d’État, Univ. Paul-Sabatier, Toulouse, 1976; per bibl.].
[For Part I, cf. 17, No. 2, 197–221 (1997; Zbl 0913.47022)].
[For Part I, cf. 17, No. 2, 197–221 (1997; Zbl 0913.47022)].
MSC:
| 47N30 | Applications of operator theory in probability theory and statistics |
| 47B07 | Linear operators defined by compactness properties |
| 62H25 | Factor analysis and principal components; correspondence analysis |
