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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeAug 20th 2014
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 20th 2014

I have added a minimum cross-link between parastatics and the existing braid group statistics

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeAug 22nd 2014

What does this mean?

[A statistic is] a function of a sample where the function itself is independent of the sample’s distribution.

This may come from Wikipedia, but the explanation there (‘the function can be stated before realization of the data’) does not help.

Since the sample is the input to the function, if the function depends on the distribution of the sample, then we just write that dependence into the definition of the function, and now we have a function that’s independent of the sample’s distribution.

More formally, if we have a function $f_S$ for each sample $S$, so that the value of the statistic at $S$ is $f_S(S)$, then we define $g(S) \coloneqq f_S(S)$, and now $g$ does not depend on the distribution of $S$.

So it seems that, mathematically, all that a statistic is, is simply a function from the set of all samples (to, say, the set of real numbers). Is this correct? Can we just say that?