# A function of sufficient statistic

by AlexStat   Last Updated October 17, 2018 17:19 PM

I'm following notes at onlinecourses and I got confused on transformation of sufficient statistics. For example, if $$X$$ is a sufficient statistic for $$\mu$$, why $$Y=X^2$$ is not a sufficient statistic for $$\mu$$? In another source Essentials of Statistical Inference by G. A. Young p. 92 $$|X|$$ is sufficient. Aren't $$X^2$$ and $$|X|$$ both many-to-one functions? Is this something to do with having single observation? Apologies in advance if this question was already asked.

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