# Questions tagged [efficiency]

A measure of the quality of a statistical estimator.

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### efficiency of variance / standard deviation

Is there any literature on the efficiency/asymptotic efficiency of the variance estimators like sample variance? I can find enough analysis about efficiency of mean estimators but nothing on that of ...
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### Maximum Likelihood Efficiency

It is a well-known fact that ML estimates are not efficient in the class of consistent, asymptotically normal estimates due to the existence of superefficient estimates. The right way to put it is ...
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### How general is the backfitting algorithm?

Hastie \& Tibshirani's original approach to fitting generalized additive models was the backfitting algorithm. For a model of the form $$y = \alpha + \displaystyle\sum_k f_k(x_k) + \epsilon$$ ...
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### Examples where method of moments can beat maximum likelihood in small samples?

Maximum likelihood estimators (MLE) are asymptotically efficient; we see the practical upshot in that they often do better than method of moments (MoM) estimates (when they differ), even at small ...
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### Asymptotic variance of GMM with efficient instrument

This question emerged from reading Wooldridge's Econometric Analysis of Cross Section and Panel Data, second edition, section 14.4.3, where the asymptotic distribution of the GMM (Generalized Method ...
585 views

Under which conditions would a researcher choose optimally when there is a trade-off between the variance and bias of an estimator? I hope this question is not too broad... Any help would be ...
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### Efficiency of beta estimates with heteroscedasticity

I need something clarified and that is when you have non-constant variance, estimates won't be biased but will be a problem when it comes to the S.E. formulas and efficiency. Therefore OLS estimates ...
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### Is there a generalization of trimean to $n$-th order (central) moments?

I think trimean is the cat's meow. Is there a generalization of this idea to $n$-th order (central) moments? Basically I live in a world where the pain of outliers vastly exceeds the pain of ...
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### Is MLE more efficient than Moment method?

I have got some small data sets (about 8 to 11 data points for each set), following Normal distribution. I would like to find out the 95% confidence interval of the 0.005 and 0.995 percentile of each ...
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### How to compute efficiency?

Suppose instead of maximizing likelihood I maximize some other function g. Like likelihood, this function decomposes over x's (ie, g({x1,x2})=g({x1})g({x2}), and "maximum-g" estimator is consistent. ...