TY - JOUR
AU1 - GIRKO, V. L.
AB -  Random Oper, and Stock. Equ., Vol. 4, No. 1, pp. 61-76 (1996) © VSP 1996 V. L. GIRKO Kiev State University, Kiev, Ukraine Received for ROSE 16 April 1995 Abstract--The asymptotic properties of normalized spectral functions of empirical covariance matrix are studied in the case of nonnormal population. It is shown that Stieltjes transforms of such function satisfy the so called canonical equation. A large series of papers is devoted to the investigation of normalized spectral functions of empirical covariance matrices (see reviews and books in the spectral theory of random matrices [1-14]). However, for many years nobody could solve the problem of deriving the equation for the Stieltjes transform of spectral functions of large order empirical covariance matrices when observations of random vector are independent. In this article, we propose a method of martingale-differences to solve this problem presented by the author in [2] and have found the equation for the Stieltjes transform of normalized spectral function. Since this equation holds for general random matrices and is often employed in applied investigations, we call it, as the similar equation in [1], a canonical spectral equation. Let the vectors JM.., . . . v af«, of dimension m 
TI - Canonical equation for the resolvent of empirical covariance matrices
JF - Random Operators and Stochastic Equations
DO - 10.1515/rose.1996.4.1.61
DA - 1996-01-01
UR - https://www.deepdyve.com/lp/de-gruyter/canonical-equation-for-the-resolvent-of-empirical-covariance-matrices-w2H0uuzfFv
SP - 61
EP - 76
VL - 4
IS - 1
DP - DeepDyve
ER -