Re: Sufficient Statistics

Dear all,
I was just reading some theoretical statistics
cs notes and found a
sentence which puzzles me:
"
the entire data is always sufficient, so we need
minimal sufficiency.


"

Do anyone know the explanation of the first part
please?

thanks very much!



If f(x, theta) is the density of the sample, where x is the sample and theta is the parameter, then T=T(x) is sufficient for theta if f(x, theta) can be factored as

f(x, theta) = g(T(x), theta)*h(x).

Set T(x)=x, g=f, and h(x)=1.

Thus T(x) = x, the entire sample is sufficient for theta.

Jack


Setting T(x) = x
.

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