A function of sufficient statistic

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

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.

enter image description hereenter image description here

Related Questions

Complete and Sufficient Statistics from Two Samples

Updated April 08, 2018 02:19 AM

complete sufficient statistic exercise

Updated April 19, 2017 17:19 PM

Sufficient statistic when $X\sim U(\theta,2 \theta)$

Updated October 24, 2018 10:19 AM

Likelihood function when $X\sim U(0,\theta)$

Updated October 24, 2018 22:19 PM