Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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 Sf_S for each sample SS, so that the value of the statistic at SS is f S(S)f_S(S), then we define g(S)f S(S)g(S) \coloneqq f_S(S), and now gg does not depend on the distribution of SS.

    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?

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)