In the computation of Sample Entropy and Approximate Entropy, the distance between any two sequences is always taken as the maximum absolute difference between the scalar components (treating the sequences to be scalars). Why is the distance defined in this way and not in any other way (e.g. the Euclidean distance)? (A paper by F Takens, "Invariants related to Dimension and Entropy" might have the answer, but I am not able to find it anywhere.)
Since sample entropy is a ratio of the number of vector pairs (of two different vectors of different lengths m and ,m+1) having a certain distance function less than some defined number, any distance function could be used.(eg Euclidean or sum of absolute scalar diff of components)
I assume the Chebyshev max absolute scalar diff distance function is used for computational simplicity.
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