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On Wikipedia, a statistic is defined to be an observable random variable ( http://en.wikipedia.org/wiki/Statistic ). However, neither of the terms statistic and observable is formally defined in the article. So what exactly is a statistic?

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  • $\begingroup$ What is wrong with a function of a sample where the function itself is independent of the sample's distribution; that is, the function can be stated before realization of the data. The term statistic is used both for the function and for the value of the function on a given sample? $\endgroup$
    – Did
    Commented Jan 4, 2013 at 23:31
  • $\begingroup$ From the information provided in your question, "statistic" is formally defined: in terms of "observable". It is just the latter term that is not defined. $\endgroup$ Commented Jan 5, 2013 at 15:05
  • $\begingroup$ @did: There's nothing wrong with it, but I was looking for a rigorous definition in terms of probability spaces and functions on them. $\endgroup$
    – Benno
    Commented Jan 6, 2013 at 12:58

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