# Questions tagged [sufficient-statistics]

A sufficient statistic is a lower dimensional function of the data which contains all relevant information about a certain parameter in itself.

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### When if ever is a median statistic a sufficient statistic?

I came across a casual remark on The Chemical Statistician that a sample median could often be a choice for a sufficient statistic but, besides the obvious case of one or two observations where it ...
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### How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean?

Let's say we have a game with two players. Both of them know that five samples are drawn from some distribution (not normal). None of them know the parameters of the distribution used to generate the ...
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### Sufficient statistics for layman

Can someone please explain sufficient statistics in very basic terms? I come from an engineering background, and I have gone through a lot of stuff but failed to find an intuitive explanation.
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### Why do we not care about completeness, sufficiency of an estimator as much anymore?

When we begin to learn Statistics, we learn about seemingly important class of estimators that satisfy the properties sufficiency and completeness. However, when I read recent articles in Statistics I ...
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### Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions

Let $\mathbf{X}= (x_1, x_2, \dots x_n)$ be a random sample from the uniform distribution on $(a,b)$, where $a < b$. Let $Y_1$ and $Y_n$ be the largest and smallest order statistics. Show that ...
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### Why a sufficient statistic contains all the information needed to compute any estimate of the parameter?

I've just started studying statistics and I can't get an intuitive understanding of sufficiency. To be more precise I can't understand how to show that the following two paragraphs are equivalent: ...
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### Sufficient statistic, specifics/intuition problems

I'm teaching myself some statistics for fun and I have some confusion regarding sufficient statistics. I'll write out my confusions in list format: If a distribution has $n$ parameters then will it ...
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### Intuitive understanding of the Halmos-Savage theorem

The Halmos-Savage theorem says that for a dominated statistical model $(\Omega, \mathscr A, \mathscr P)$ a statistic $T: (\Omega, \mathscr A, \mathscr P)\to(\Omega', \mathscr A')$ is sufficient if (...
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