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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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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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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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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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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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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How does Bayesian Sufficiency relate to Frequentist Sufficiency?
The simplest definition of a sufficient statistics in the frequentist perspective is given here in Wikipedia. However, I recently came across in a Bayesian book, with the definition $P(\theta|x,t)=P(\...
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Puzzled by the definition of sufficient statistics in Mood, Graybill, and Boes
I am learning about sufficient statistic from Mood, Graybill, and Boes's Introduction to the Theory of Statistics. I am slightly confused by the book's definition of a sufficient statistic for ...
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Basic intuition about minimal sufficient statistic
As stated by Wikipedia:
A sufficient statistic is minimal sufficient if it can be represented as a function of any other sufficient statistic. In other words, $S(X)$ is minimal sufficient if and ...
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When using the likelihood function, where does the indicator function come from?
For finding sufficient estimators and MLE's, there are certain distributions that require the indicator function such as the uniform distribution. Where does it come from in simple language? and for ...
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Can this statistic be shown not to be sufficient for $\theta$?
This problem comes from Casella and Berger, who do not rigorously demonstrate (in their solution key) that the statistic is not sufficient.
Let $X_1,\dots,X_n$ be a random sample from a population ...
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Sufficient statistic for bivariate or multivariate normal
Here on page 7, example 2.7. The claim is that sufficient statistics for $d$ dimensional multivariate normal $\mathbf{x}_i \sim N(\vec{\mu}, \Sigma)$ is $$\left(n^{-1}\sum_{i=1}^n \mathbf{x}_i, \hat{\...
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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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Sufficiency or Insufficiency
Consider a random sample $\{X_1,X_2,X_3\}$ where $X_i$ are i.i.d.
$Bernoulli(p)$ random variables where $p\in(0,1)$. Check if
$T(X)=X_1+2X_2+X_3$ is a sufficient statistic for $p$.
Firstly, how ...
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