  We study the effects of the finite number of experimental data on the
computation of a generalized fluctuation-dissipation relation around a
nonequilibrium steady state of a Brownian particle in a toroidal optical trap.
We show that the finite sampling has two different effects, which can give rise
to a poor estimate of the linear response function. The first concerns the
accessibility of the generalized fluctuation-dissipation relation due to the
finite number of actual perturbations imposed to the control parameter. The
second concerns the propagation of the error made at the initial sampling of
the external perturbation of the system. This can be highly enhanced by
introducing an estimator which corrects the error of the initial sampled
condition. When these two effects are taken into account in the data analysis,
the generalized fluctuation-dissipation relation is verified experimentally.
