Flyvbjerg and Petersen demonstrated that the sequence \{e_k\}_{k=0}^{d-1} is decreasing, and conjecture that the term e_k can be made as small as we would like by making k (and hence d ) sufficiently large. The sequence is decreasing. It means we can apply blocking transformations until e_k is sufficiently small, and then estimate \mathrm{var}(\overline{X}) by \widehat{\sigma}^2_k/n_k .
For an elegant solution and proof of the blocking method, see the recent article of Marius Jonsson (former MSc student of the Computational Physics group).