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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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Sample mean of Bernoulli trials is admissible under squared loss

Let $X_1,\ldots,X_n$ be i.i.d. Bernoulli trials with probability $\theta\in(0,1)$, and let $L:(0,1)\times[0,1]\to\mathbb{R}$ be the squared loss function, i.e. $L(\theta,a)=(\theta-a)^2$. I am trying ...
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When is it better to have an unbiased estimator instead of one that has a smaller risk?

I just learned that for $X_1, \ldots X_n \sim N(\mu, \sigma^2)$ i.i.d, the sample variance $\frac{1}{n-1} \sum_{i=1}^n (X_i - \bar X)^2$ is unbiased, and it is in fact UMVUE. However, it is not ...
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Why are fisher-scoring estimates of the fixed-effects not used to calculate empirical bayes estimates of random-effects? Are they in-admissible?

Why is it not practiced using estimates of fixed-effects from fisher scoring used to calculate GEE coefficients to estimate random-effects via empirical bayes? We have another estimate of $\theta$ in ...
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Why has the admissibility of the Graybill–Deal estimator eluded a proof for so long?

The Graybill–Deal estimator is used to estimate the shared mean of two normals with unknown variances. I understand the literature has proven it is unbiased, but a proof of admissibility has not yet ...
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James-Stein-style estimator when we place greater importance on some components

The James-Stein estimator allows us to get a better overall estimate of a mean vector (length $\ge 3$) than we would be able to get by estimating the components independently. My intuition is that, ...
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Is a constant ever inadmissible?

For now, assume square loss. Let's estimate some parameter $\theta$, such as $\theta = \mu$ in $N(\mu, 1)$. Is there ever a case where there is no such $c$ to make $\hat{\theta} = c$ an admissible ...
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Is $\frac1{n+1}\sum_{i=1}^n(X_i-\overline X)^2$ an admissible estimator for $\sigma^2$?

Consider a sample $X_1,X_2,\ldots,X_n$ from a univariate $N(\mu,\sigma^2)$ distribution where $\mu,\sigma^2$ are both unknown. Then it is known that under squared error loss, the sample variance $s^2=\...
StubbornAtom's user avatar
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General Strategy to show an estimator is admissible?

I am getting into decision theory and I was wondering if there was a general way to check if a an estimator is admissible. (PS This question might have already been asked, sorry if that is the case I ...
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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 ...
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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 ...
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Empirical Bayes (In)Admissibility

Most of the time, sticking to a pure Bayesian approach to statistics with proper priors, leads to admissible estimators. Nevertheless, there is a good reason to use Empirical Bayes in many cases, and ...
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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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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 ...
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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 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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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 ...
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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,\...
Sepideh Bakhoda's user avatar
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1 answer
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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
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