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Admissible estimator: there is no other estimator for which the risk is $\leq$ for all possible true values of the target parameter.

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I would like to hear about a few simple empirical bayes estimators that are admissible for high (i.e. at least 3) dimensional parameter space. What are some textbook lollipop examples to study for ...
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Let us say, I have a distribution with some unknown parameter and I find the MLE of the parameter. I prove that the MLE is inadmissible using some other estimator. Why is this not in a contradiction ...
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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 ...
277 views

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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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 ...
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### 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 ...
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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 $x \in \mathbb{... 0answers 103 views ### Well structured data In the paper "Admissible clustering procedures" the authors Van Ness and Fisher (1971) have explained well structured data as follows: Data is said to be well structured if it has exact tree ... 2answers 176 views ### Admissibility under the loss function Suppose$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,\...
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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 ...
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### 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 ...
169 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 ...
128 views

### Why is the MLE/OLS estimator so common in regression despite inadmissibility? [closed]

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 ...
### 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