# Questions tagged [efficiency]

A measure of the quality of a statistical estimator.

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### How to show mathematically that random effects are more efficient than fixed effects?

I have read in several places now that random effects estimators are more efficient than fixed effects estimators, in particular here I’ve searched this site and Google and couldn’t find this result. ...
87 views

### 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 ...
9 views

### Questions about efficiency of estimators with longitudinal data

I'm modelling data with repeated observations; I'm reading up on options and pitfalls, and have a few questions. Coefficient estimates are still unbiased and consistent in the presence of ...
183 views

### Asymptotic efficiency of IQR

I was wondering about the asymptotic efficiency of the Interquartile Range (IQR) in the Gaussian case. I have calculated it empirically using a Monte Carlo estimator, and it appears to be equal to ...
48 views

### Is the smooth transformation of an asymptotically efficient estimator still asymptotically efficient?

Suppose I have an estimator $\widehat{\theta}$ that is asymptotically efficient (for example, it could be the MLE of the mean $\mu$ and variance $\sigma^2$ of $Normal(\mu,\sigma^2)$). Suppose I also ...
33 views

### 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 ...
20 views

91 views

### Counterexamples: Minimax but not efficient, efficient but not minimax

Are there examples of estimators that are minimax, but not efficient? Perhaps, to be more concrete, any of the following: (strong) Estimator sequence for each $n$ that is minimax but does not match ...
20 views

### Is there any advantage to PPS sampling if, in the end, you sample the same number of your sub quantity?

PPS sampling (Probability-proportional-to-size sampling), it seems to me, is based on the scenario where you are limited to sampling a fixed number, $n$, units of observation containing some varying ...
12 views

### Many crossed-random effects increase multicollinearity, decreases efficiency or consistency or introduces bias?

Many crossed-random effects increases multicollinearity, decreases efficiency or consistency or introduces bias? What are the trade-offs of using many random-effects? 