Spectral properties of sample covariance matrices

The expectation value of the resolvents of sample covariance matrices and the variance of their matrix elements are investigated. It is assumed only that variables have zero expectation values and the maximal fourth moment of variables exists. The principal spectral equations obtained earlier only in the form of limit formulas are derived with upper estimates of the remainder terms, accurate up to absolute constants. The remainder terms prove to be small for large sample size and a small value of a special measure of the quadratic forms variance.