All Questions
Tagged with estimators efficiency
25
questions
2
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0
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46
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No Existence of Efficient estimator
I need to prove that given $(X_1,...,X_n)$ from the density $$\frac{1}{\theta}x^{\frac{1}{\theta}-1}1_{(0,1)}$$ no efficient estimator exists for $g(\theta)$=$\frac{1}{{\theta}+1}$.
I have shown that ...
0
votes
0
answers
22
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Is Coefficient of Variation a valid measure of relative efficiency?
I'm wondering if it is always valid to use Coefficient of Variation (CV) to determine relative efficiency of parameter estimators, and to compute statistically equivalent sample sizes based on that ...
- 1,162
0
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0
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18
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What is the difference between unbiasedness, consistency and efficiency of estimators? How are these interrelated among themselves? [duplicate]
!Efficiency(https://stackoverflow.com/20240427_193105.jpg). Given snapshot of the book states that among the class of consistent estimators, in general, more than one consistent estimator of a ...
- 1
5
votes
2
answers
128
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Sufficient conditions for asymptotic efficiency of MLE
Maximum-likelihood estimators are, according to Wikipedia, asymptotically efficient, that is they achieve the Cramér-Rao bound when sample size tends to infinity. But this seems to require some ...
- 1,099
3
votes
1
answer
144
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Estimating ratio of regression coefficients
What is the best method of estimating a ratio of regression coefficients $\beta_1/\beta_2$ under the usual assumptions / in practice? I have two relatively well approximated signals $X_1, X_2$ and ...
3
votes
0
answers
39
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Adjusting confidence interval of estimator by efficiency
Summary: If we have an unbiased MLE $\widehat{\sigma_1}$ of an exponential distribution parameter, and the confidence intervals for its estimates are given by the $\chi^2$ distribution; and we find ...
- 1,162
4
votes
2
answers
3k
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What does asymptotic efficiency mean?
I read some comparison articles, and always find "asymptotic efficiency," "asymptotically less efficient," and "asymptotically normal."
I am really confused about the ...
- 650
2
votes
1
answer
330
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Monte Carlo in R simulation for Efficiency [closed]
An exercise displayed in the image below shows example of finding the efficiency of an estimator. I am trying to replicate this example in R using monte carlo. Y1,Y2,Y3 are random samples of normal ...
1
vote
1
answer
230
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Is the Hodges-Lehmann estimator 'optimal' for estimating the location parameter of Logistic distribution?
Is the Hodges-Lehmann estimator $\hat\theta_{HL}=\operatorname{median}\limits_{1\le i\le j\le n}\left\{\frac{X_i+X_j}{2}\right\}$ in some sense 'optimal' for estimating the location parameter $\theta$ ...
- 11.5k
1
vote
0
answers
166
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Asymptotic efficiency of estimators of autoregressive models
Are OLS or MLE estimators of autoregressive model asymptotically efficient if errors are i.i.d?
Consider the case of an AR(1) model $$x_t=\alpha x_{t-1} + \epsilon_t$$
with $\epsilon_t$ ~ $i.i.d. N(0,\...
- 51
2
votes
0
answers
34
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Are these statements about the maximum likelihood estimator and efficiency correct?
I'm trying to understand efficiency and its relation with maximum likelihood estimators so I need someone to confirm or correct these statements I deduced :
1/ If the maximum likelihood estimator ...
- 155
4
votes
1
answer
243
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Which is a better estimator, averaged functions vs. A function of an average?
Problem:
Assume that we want to estimate $f(\theta)$ with a pre-specified strictly increasing function $f$ and a parameter $\theta$.
Let $\hat{\theta}_1$ and $\hat{\theta}_2$ be unbiased estimators ...
- 538
1
vote
0
answers
74
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Is the $\sigma$ estimator more efficient than the $\mu$ estimator?
Are my empirical findings correct? How to get the same result analytically?
I studied the efficiency of the mean and standard dev estimators:
$$\mu_n=\sum \frac {x_i} {n}\space\space\space\space\...
- 1,230
0
votes
1
answer
338
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Exponential family and efficient estimator
In my lecture notes there is the notion of efficiency related to the exponential family. More precisely, the lecturer stated that for an exponential family an efficient estimator always exists. How is ...
10
votes
1
answer
5k
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When can't Cramer-Rao lower bound be reached?
The Cramer-Rao lower bound (CRLB) gives the minimum variance of an unbiased estimator. One sentence in the wiki page says "However, in some cases, no unbiased technique exists which achieves the bound....
- 220