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It's a homework question, but I just have no idea about it ...

Let X_{1} ,... , X_{n} be random variables according to a distribution having joint density f(x_{1}-\theta ,...,x_{n}-\theta ),where \theta \in R is a location parameter. Assume that there exists a complete sufficient statistics S(X_{1} ,... , X_{n} ) for theta. Prove that the Pitman estimator

\delta^{*}(X_{1},...,X_{n})=\frac{\int _{R}\theta f(X_{1}-\theta ,...,X_{n}-\theta) d\theta }{\int _{R} f(X_{1}-\theta ,...,X_{n}-\theta) d\theta }

is itself complete sufficient.

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  • $\begingroup$ Add the self-study tag. $\endgroup$ – Michael R. Chernick Jun 5 at 3:20
  • $\begingroup$ Please use MathJax for typesetting math here. $\endgroup$ – StubbornAtom Jun 6 at 13:10

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