All Questions
Tagged with sufficient-statistics point-estimation
12
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When are Bayes estimators injective as a function of sufficient statistics?
I know that Bayes estimators can be written only as a function of sufficient statistics. When are those functions injectives? That is, when can I say that, given a bayes estimator $\delta (\cdot)$ and ...
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How does reparametrization of the Fisher information matrix change the variance expression for the sufficient statistics?
If I have an exponential family distribution of the form $$p_{\theta}(x) = e^{\theta^T\cdot t(x) - \psi(\theta)},$$ where $\theta$ is a vector of parameters, $t(x)$ is a vector of sufficient ...
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FInding a complete and sufficient statistic
I am attempting to learn how to find a complete and sufficient statistic. So, I am working on this problem for class:
Let $X_1, \cdot\cdot\cdot,X_n$ be a random sample from the pdf $f(x_i|u)=e^{-(x-\...
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nonexistence of a sufficient statistic
Let $X_1,X_2,\dots,X_n$ be a random sample from a $\Gamma(\theta,\theta)$ distribution. Then
$$
\prod_{i=1}^n f(x_i;\theta) = \frac{1}{\Gamma(\theta)^n\theta^n}(\prod_{i=1}^n x_i)^{\theta-1}e^{-\frac{...
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Minimal sufficient statistic whose dimension is less than dimension of parameter [duplicate]
Consider following example:
Suppose $ X\sim N(0, \sigma^2) $,
consider a random sample of size one from this population.
Clearly $X$ is sufficient statistic but $ |X| $ is minimal sufficient ...
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285
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sufficient statistic for n-point distribution that depends of one parameter
I'm studiying the concept of sufficient statistic, but I have a question that I can't resolve... I hope someone can help me.
My question is the next:
I suppose that I do n independent trials with m ...
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Are there examples of non exponential family distributions with sufficient statistics?
In Casella Berger's Statistical Inference, they observe that it is rare to find 'a sufficient statistic with dimension smaller than the sample' (section 6.2.1). Although rare, are there examples of ...
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Does the UMVUE have to be a minimal sufficient statistic?
I'm studying point estimation and I have found this question that seems pretty tricky to me.
If $T$ is a minimal sufficient statistic for $\theta$ with $E(T) = \tau(\theta)$, can you say that $T$ ...
- 3,099
8
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Are complete statistics always sufficient?
I know that a complete sufficient statistic $T$ is such that
1) $T$ is sufficient for $\theta$, unknown parameter and 2) $T$ is complete.
So, is it always the case? If the answer is not, what ...
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complete sufficient statistic exercise
I have to find complete sufficient statistic of the following pdf
$$f(x|\theta)=\frac{\theta}{(1+x)^{(1+\theta)}},\quad 0<x<\infty,\theta>0.$$
My Attempt:
The joint density
$$f(\mathbf x|\...
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12
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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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2
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How to find conditional distribution for Rao-Blackwellizing an estimator?
Let's say I have an unbiased estimator $u(\underline x)$ for function $v(\theta)$ where $\theta$ is a parameter of the distribution of $x$, and $T(\underline x)$ which is a sufficient statistic for $\...
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