  Recently discovered identities in statistical mechanics have enabled the
calculation of equilibrium ensemble averages from realizations of driven
nonequilibrium processes, including single-molecule pulling experiments and
analogous computer simulations. Challenges in collecting large data sets
motivate the pursuit of efficient statistical estimators that maximize use of
available information. Along these lines, Hummer and Szabo developed an
estimator that combines data from multiple time slices along a driven
nonequilibrium process to compute the potential of mean force. Here, we
generalize their approach, pooling information from multiple time slices to
estimate arbitrary equilibrium expectations. Our expression may be combined
with estimators of path-ensemble averages, including existing optimal
estimators that use data collected by unidirectional and bidirectional
protocols. We demonstrate the estimator by calculating free energies, moments
of the polymer extension, and the metric tensor for thermodynamic length in a
model single-molecule pulling experiment. Compared to estimators that only use
individual time slices, our multiple time-slice estimators yield substantially
smoother estimates and achieve lower variance for higher-order moments.
