# When are order statistics not sufficient?

Lehmann and Casella (http://www.springerlink.com/content/978-0-387-98502-2) state it as an example (Example 1.6.10) that for arbitrary continuous distributions, the order statistics are always sufficient. Is this a theorem, or are pathological examples known to exist? Are there necessary conditions for the order statistics to constitute a set of sufficient statistics?

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 Sufficient for what parameter(s)? – onestop Dec 21 '11 at 20:28 every order statistic? If you know every order statistic then you know the entire data set. – Macro Dec 21 '11 at 20:46 @Macro Yes, but knowing the entire data set is not the same as knowing all the information in the sample. – fg nu Dec 21 '11 at 21:09 @onestop Good point. For the parameters of the prototypical pdf of an iid sample. – fg nu Dec 21 '11 at 21:11