Does the absolute value of $x$ is sufficient statistic to the continuous distribution which is symmetric about $y$ axis? e.g. the standard normal.
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The question makes no sense in its present form, since a single distribution, e.g. the standard normal, has no free parameters, and the concept of a sufficient statistic refers to families of distributions with free parameters.
The absolute value $|x|$ is a sufficient statistic for a single sample $x$ from a family of distributions parametrized by $\theta$ if $f_\theta(-x)=f_\theta(x)$ for all $\theta$.
joriki
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I made mistake here, but how can I prove this? Can u help me? Thanks. – Jakoer Oct 08 '15 at 23:21
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@Jakoer: What theorems or definitions do you know that could allow you to conclude that something is a sufficient statistic? – joriki Oct 09 '15 at 01:48