Re: Minimal sufficient statistic

Karl Ove Hufthammer wrote:
Wei:

Let X1, ..., Xn be i.i.d. normal with both mean and variance Theta,
where Theta >0 is the unknown parameter. What is the minimal
sufficient statistic for Theta?

I got Sum(Xi ^2) as the minimal sufficient statistic for Theta. But
the answer seems to be the tradtional (X bar, S^2),

I get the same answer as you. Are you sure the question was not
about
i.i.d. normals with mean and *standard deviation* theta?

This is a fairly standard example (known coefficient of variation).
See Cox & Hinkley Theoretical Statistics Example 2.21 who agree that
(sum Xi, sum Xi^2), or variants of this pair, is mimimal sufficent.
They draw this conclusion by writing the distribution as part of the
exponential family.

Try a google on "known coefficient of variation".

David Jones


.

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