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October 20th, 2014, 07:14 AM   #1
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sufficiency

Let X1,...,Xn be iid with density $\displaystyle f(x;\theta )=\frac{2}{3\theta}(1-\frac{x}{3\theta})$ for $\displaystyle 0<x<3\theta$ and let $\displaystyle \widehat{\theta}=\widehat{X}$ be an estimate of $\displaystyle \theta$.

I determined that the estimator is unbiased and consistent. But now I have to determine wheter it is sufficient. I tried to factor the jpd function, but I got $\displaystyle (1-\frac{x}{3\theta})^{n}$ and I don't know how to handle... Trying a counter example I only did in discrete cases before, so I don't know how to do that as wel. Can someone give me a hint for a approach?

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