On fits to correlated and auto-correlated data

Observables in particle physics and specifically in lattice QCD calculations are often extracted from fits. Standard ${\chi }^2$ tests require a reliable determination of the covariance matrix and its inverse from correlated and auto-correlated data, a challenging task often leading to close-to-singular estimates. These motivate modifications of the definition of ${\chi }^2$ such as uncorrelated fits. We show how the goodness-of-fit measured by their p-value can still be estimated robustly for a broad class of such fits.