# 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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### 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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### Sufficient statistics for Uniform $(-\theta,\theta)$

So, I know that $\max(-X_{(1)},X_{(n)})$ is a sufficient statistic for the parameter $\theta$. But can I also say that $(X_{(1)},X_{(n)})$ are jointly sufficient for the parameter $\theta$ ? In other ...
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### What does it mean that a statistic $T(X)$ is sufficient for a parameter?

I am having a hard time understanding what a sufficient statistic actually helps us do. It says that Given $X_1, X_2, ..., X_n$ from some distribution, a statistic $T(X)$ is sufficient for a parameter ...
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### Is there a difference between Bayesian and Classical sufficiency?

The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? ...
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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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### Solution to German Tank Problem

Is there a formal mathematical proof that the solution to the German Tank Problem is a function of only the parameters k (number of observed samples) and m (maximum value among observed samples)? In ...
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### Why does a sufficient statistic contain 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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### Can the Fisher factorization theorem be understood as a product of densities?

Let $T$ be some random variable on a probability space $\Omega$. Then we have, for $x\in\Omega$: $$P(x) = P(x|T=T(x))P(T = T(x))$$ This equation is nonsense in an arbitrary probability space but ...
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