  The inference procedure for the mean of a stationary time series is usually
quite different under various model assumptions because the partial sum process
behaves differently depending on whether the time series is short or long-range
dependent, or whether it has a light or heavy-tailed marginal distribution. In
the current paper, we develop an asymptotic theory for the self-normalized
block sampling, and prove that the corresponding block sampling method can
provide a unified inference approach for the aforementioned different
situations in the sense that it does not require the {\em a priori} estimation
of auxiliary parameters. Monte Carlo simulations are presented to illustrate
its finite-sample performance. The R function implementing the method is
available from the authors.
