Bootstrap method failing where blocking works I'm computing an average of individual samples that are not entirely independent and need an estimate for the true standard deviation. According to Newman and Barkema's book the most reliable method will be Bootstrap sampling (see section 3.4.3), where you don't have to worry about the samples being independent and which should give an estimate of the standard deviation of the mean $\sigma_m\approx\sigma\ /\sqrt{n}$ where $n$ is the number of samples.
However I proceed to compute the average a number of times so that I get a brute force estimate of the actual $\sigma_m$, and it turns out that the bootstrap is consistently underestimating this. 
In itself that is maybe not so strange; the bootstrap being an estimate. But the weird thing is that if I use the blocking (or binning) method (see 3.4.2) I get a much better estimate - while according to Newman and Barkema this should be a much more primitive method.
In fact the bootstrap consistently gives an estimate very close to the naive $\sigma_m\approx\sqrt{\big(\ \overline{x^2}-\overline{x}^2\ \big)\ /\ n}$.
Any idea what's going on?

The naive bootstrap method (where the original data is resampled with replacement) does indeed systematically underestimate the error of correlated data as discussed for example in Remark 2.1 on page 1192 in A. Singh, The Annals of Statistics 9, 1187-1195.
I'm not at all an expert in this field, and came across the same problem as the original poster, also following the book by Newman and Barkema. My interpretation after reading the original literature and playing with data is that the description in Newman and Barkema is rather misleading.
