Questions tagged [admissibility]
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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questions
4
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1answer
166 views
Admissible Empirical Bayes Examples
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 ...
2
votes
0answers
31 views
Inadmissible MLE
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 ...
10
votes
0answers
219 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
votes
2answers
277 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 ...
4
votes
0answers
147 views
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 ...
8
votes
1answer
377 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
votes
1answer
223 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{...
0
votes
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 ...
4
votes
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,\...
5
votes
1answer
145 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
votes
1answer
762 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
votes
0answers
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 ...
3
votes
1answer
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 ...
3
votes
2answers
1k 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 ...
5
votes
1answer
156 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
