On the use of the covariance matrix to fit correlated data

Abstract

Best fits to data which are affected by systematic uncertainties on the normalization factor have the tendency to produce curves lower than expected if the covariance matrix of the data points is used in the definition of the χ 2. This paper shows that the effect is a direct consequence of the hypothesis used to estimate the empirical covariance matrix, namely the linearization on which the usual error propagation relies. The bias can become unacceptable if the normalization error is large, or a large number of data points are fitted.