The asymptotics of Stieltjes transforms of singular spectral functions. (English. Russian original) Zbl 0834.62018

Girko, V. L.; Stepakhno, I. V.

Theory Probab. Math. Stat. 46, 39-45 (1993); translation from Teor. Jmovirn. Mat. Stat. 46, 42-50 (1992).

Summary: We study the asymptotics of the Stieltjes transforms of the spectral functions of the eigenvalues of a matrix \(A= (a_{ij})\), \(i=1, \dots, n\), \(j=1, \dots, m\), by the method of general statistical analysis assuming known only the random variables \(X_i\), \(i=1, \dots, s\), which are independent observations of the matrix \(A+ \Xi\), where \(\Xi\) is a stochastic matrix.

MSC:

62E20	Asymptotic distribution theory in statistics
62H10	Multivariate distribution of statistics
15A18	Eigenvalues, singular values, and eigenvectors
15B51	Stochastic matrices

Keywords:

G-estimation of eigenvalues; Cauchy distribution; martingale; Stieltjes transforms; spectral functions