Convergence of large deviation estimators,
C. Rowher, F. Angeletti, H. Touchette, Phys. Rev. E, (2015), 52104, Abstract
We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium,nonequilibrium,and man-made stochastic systems. We give conditions for the convergence of these estimators with sample size,based on the boundedness or unboundedness of the quantity sampled,and discuss how statistical errors should be defined in different parts of the convergence or self-averaging region. Our results shed light on previous reports of ‘phase transitions’ in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from experimental data.