\(G_{25}\)-estimators of principal components. (English. Russian original) Zbl 0764.62050

Girko, V. L.

Theory Probab. Math. Stat. 40, 1-10 (1990); translation from Teor. Veroyatn. Mat. Stat., Kiev 40, 3-11 (1989).

Summary: For the principal components \((h_ k,\xi)\), where the \(h_ k\) are eigenvectors of the covariance matrix \(R\) and \(\xi\) is an \(m_ n\)- dimensional observable random vector, we give Stieltjes transforms, and for these we find \(G\)-estimates under the Kolmogorov condition \(\lim_{n\to\infty} m_ n n^{-1}<1\). We prove the asymptotic normality of these estimates.

MSC:

62H25	Factor analysis and principal components; correspondence analysis
62H12	Estimation in multivariate analysis
62F12	Asymptotic properties of parametric estimators

Keywords:

principal components; eigenvectors; covariance matrix; Stieltjes transforms; \(G\)-estimates; Kolmogorov condition; asymptotic normality