  In this paper, we derive higher order Edgeworth expansions for the finite
sample distributions of the subsampling-based t-statistic and the Wald
statistic in the Gaussian location model under the so-called fixed-smoothing
paradigm. In particular, we show that the error of asymptotic approximation is
at the order of the reciprocal of the sample size and obtain explicit forms for
the leading error terms in the expansions. The results are used to justify the
second-order correctness of a new bootstrap method, the Gaussian dependent
bootstrap, in the context of Gaussian location model.
