# Questions tagged [efficiency]

A measure of the quality of a statistical estimator.

154 questions
Filter by
Sorted by
Tagged with
4 views

### Maximum likelihood estimator when the Fisher information matrix is not invertible?

It is known that maximum likelihood estimator (MLE) is asymptotically efficient, i.e., $\sqrt{n\,}\,\left( \widehat{\theta \,}_{\mathrm{mle}}-\theta _0 \right)$ converges in distribution to a ...
• 187
46 views

### 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 ...
1 vote
35 views

### Small sample MLE vs OLS efficiency

MLE estimates are asymptotically efficient. Both MLE and OLS estimates are asymptotically normal and for many distributions their limiting variances coincide (information for one observation being the ...
• 141
22 views

### 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
18 views

### 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 ...
23 views

### What is known about the (in)efficiency of true score variance estimation?

In classical test theory, an observed score $X$ is defined as $$X = T + E$$ where $T$ represents the individual true score and $E$ represents the individual error score. In this context $T$ may be ...
• 143
15 views

### Understanding Asymptotic Relative Efficiency and how to compute it

I am learning about asymptotic relative efficiency (ARE) in class, and I am trying to understand exactly how to compute the ARE. From my understanding, asymptotic relative efficiency refers to ...
• 345
128 views

### 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
27 views

### Are these two estimated regression coefficient asymptotically equivalent? If not, which one is more efficient?

Suppose I have $Y=\beta_1X_1+\beta_2X_1X_2+g(X_2)+u$, where $E(u|X_1,X_2)=0$ and $S=g(X_2)+e$ with $E(e|X_2)=0$. I have a random sample $\{Y_i,X_{1i},X_{2i},S_i\}_{i=1}^n$. Suppose I first use a ...
• 2,966
1 vote
36 views

### How can I rigorously quantify the increase performance due to additional parameters?

I am trying to evaluate a novel dimensionality reduction technique. Specifically, we start with a data set with around 1,000 features/covariates per observation. My technique maps this down to 12. ...
• 13
78 views

### 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. ...
• 741
144 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 ...
11 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 ...
• 741
372 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 ...
• 61
72 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 ...
• 2,966
39 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 ...
• 1,162
23 views

• 51
410 views

### Data-efficiency vs sample-efficiency

I noticed that in the context of RL, people call the ability to learn from little data "sample-efficiency". However, in the context of supervised learning, it is called "data-efficiency&...
• 1,337
43 views

### An efficient estimator can be biased? [duplicate]

Can someone explain to me whether an efficient estimator can be biased? What I've read so far seems to be always about efficiency being a property being alluded to unbiased estimators but I was ...
• 23
324 views

### Efficient influence function in proportional hazards model

I was hoping someone could help me with this problem in the cox proportional hazards model. I am given the following setup. T is a non-negative random variable with continous distribution and hazard ...
• 63
49 views

• 2,966
1 vote