Designed for processing big permutations, all proposed algorithms are able to do a partial enumeration of traces for permutations which cannot be processed by the actual algorithms for total trace enumeration, that is, BFA and DFA with or without permutation grouping.
As discussed in Mercade et al. [ 30], permutation techniques cannot be applied here because an infinitesimal genetic value is included.
However, permutation methods cannot be used in this setup, since the distributions of the test statistics and the resampling statistics do not coincide, not even asymptotically (Pauly M, Asendorf T, Konietschke F: Permutation tests and confidence intervals for the area under the ROC curve, submitted).
However, in cases where parametric assumptions cannot be made, nonparametric permutation testing may provide an alternative way of determining the sampling distribution.
The time series in the top left panel of Figure 2 cannot be distinguished from its permutations and thus is unsuitable for the purposes of forecasting.
The likelihood function remains constant given a permutation of their individual components, and the estimation parameters cannot be obtained.
The existence of one or more bad components in a permutation indicate exactly those situations where the lower bound cannot be met [ 1].
Otherwise, all the permutations represented by the resulting tree are non-valid, because conflicting restrictions cannot be fulfilled.
To put it quickly, a permutation of a pair of elements that are arbitrarily far apart cannot be ensured otherwise.
However, the classic bootstrap cannot be applied directly to rearrangement data because the collection of permutations forms a single character a single rearrangement or duplication can affect an entire permutation.
