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?
Tell me more
×
Cross Validated is a question and answer site for
statisticians, data analysts, data miners and data visualization experts. It's 100% free, no registration required.
|
|
The order statistics are just the sorted data values, so for any case where the data is univariate iid, the order statistics have the exact same information as the original data (just in a different order). If the order in the data matters (not iid, e.g. time series) then the order statistics don't have that information and that would be one case where they were not sufficient. Another case would be non-univariate cases, the order statistics of X and the order statistics of Y would be sufficient for the X and Y distributions seperately, but not for covariance or correlation parameters. |
|||
|
