Statistical properties of the estimator using covariance matrix

Abstract

The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic cases (when systematic errors on the fitted parameters are not extremely large comparing with the statistical ones) and its dispersion is always smaller, than the dispersion of the simplified $χ^2$ estimator applied to the correlated data. The CME bias is negligible for the realistic cases if the covariance matrix is calculated during the fit iteratively using the parameter estimator itself. Analytical formula for the covariance matrix inversion allows to perform fast and precise calculations even for very large data sets. All this allows for efficient use of the CME in the global fits.