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Questions tagged [admissibility]

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172 views

Empirical Bayes (In)Admissibility

Sticking to a pure Bayesian approach to statistics with proper priors most of the time leads to admissible estimators. Nevertheless there is good reason to use Empirical Bayes in many cases, and the ...
2
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2answers
136 views

Admissible Bayes Rule

In the following wikipedia entry https://en.wikipedia.org/wiki/Admissible_decision_rule it is written that "Bayes rules with respect to proper priors are virtually always admissible" What do they ...
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0answers
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Is an inadmissible estimator necessarily dominated by some admissible estimator

Basic example: $X$ has a $p$-variate iid standard Normal distribution; the sample mean is not admissible if $p>2$ and is dominated by the Stein shrinkage estimator. However, the Stein shrinkage ...
6
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1answer
273 views

Model with admissible estimator(s) that are not the Bayes estimator for any choice of prior?

Every Bayes estimator is admissible, to the best of my knowledge. (Related questions - 1,2.) I recall my professor mentioning once during a lecture that, at least as rough intuition, the converse is ...
4
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1answer
200 views

How to choose loss function (in unbounded parameter space)?

How does one choose a loss function for a given problem? (I've looked through stackexchange, and I haven't been able to find a thread that discusses this.) Let say I observe some data $x \in \mathbb{...
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95 views

Well structured data

In the paper "Admissible clustering procedures" the authors Van Ness and Fisher (1971) have explained well structured data as follows: Data is said to be well structured if it has exact tree ...
5
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2answers
163 views

Admissibility under the loss function

Suppose $X_1 , ..., X_n$ are random samples of exponential distribution with mean $\theta$. Determine $a$ and $b$ such that $a\sum_{i=1}^n X_i +b$ be admissible under the loss function $L(\theta,\...
5
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1answer
100 views

Admissibility of Bayes estimators

I have the following questions. They are not homework problems, but they are things that the professor said that I should wonder about. I suspect that I will have to deal with this on an exam in the ...
4
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1answer
587 views

On the proof of admissibility of constant estimators under squared loss

The question concerns the discussion in Wasserman, All of Statistics, Section 13.6. He defines: An estimator $\hat{\theta}$ is inadmissible if there exists another rule $\hat{\theta}'$ such that ...
6
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0answers
158 views

Why is Wald's decision theory not universally recognized as the foundation of statistics?

This is somewhat ill-defined, but: Why is Wald's decision theory not universally recognized as the foundation of statistics? I gather (or maybe I infer) that it was formulated to put frequentist and ...
2
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1answer
105 views

Why is the MLE/OLS estimator so common in regression despite inadmissibility?

Why is regression so commonly used if the OLS estimator for the vector of regression coefficients is inadmissible under the squared error loss function? Is it because of its historical popularity or ...
3
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2answers
977 views

Admissible Estimator for Linear Regression

Is there an admissible estimator for a linear regression model with many parameters without restricting the parameter space? Admissibility will be with respect to Mean Square Error on the regression ...
4
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1answer
112 views

showing that $\bar{X}$ is inadmissible by comparing with $\max(\bar{X},2)$ under squared error loss function

suppose $X_1,X_2,\ldots,X_n$ be a random sample of $N(\theta,1), \theta>2$. how can I show $\bar{X}$ is inadmissible estimator Compared to $\max(\bar{X},2)$ under Squared error loss function