Questions tagged [efficiency]

A measure of the quality of a statistical estimator.

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Calculating "relative efficiency" of a single estimator in two samples from different processes

I want to assess how well the multilevel AR(1) model performs on not-so-long time series wherein the AR(1) model assumptions are violated. I have three data generating processes (say, $P_1$, $P_2$, ...
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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 ...
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Relative efficiency of two estimators for the cardinality of a set from which we sample without replacement

I would like to check my understanding of the relative efficiency for the following estimators for the problem of estimating the cardinality of a set, from which you sample without replacement; i.e. ...
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fixed effects model: efficiency

Suppose I have flight delay data for multiple airlines. I want to estimate the fixed-effects model and choose aircraft to be a cross-sectional unit. Therefore, I include aircraft fixed effects in the ...
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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 ...
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Expected variance of biased estimators

Suppose that $\mu$ is an unknown $k$-vector, which one seeks to guess. You observe $n$ i.i.d. normal variates $x_i \sim \mathcal{N}\left(\mu,\Sigma\right)$, say stacked in the matrix $X$, then produce ...
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Using calculus of variations to deduce lower bound on Pitman efficiency (asymptotic relative efficiency) between $t$-test and sign test

Let $Y_1,...,Y_n$ be iid draws from a location family $\{f(\cdot - \theta) : \theta \in \mathbb{R}\}$. $f$ is a symmetric density w.r.t. the Lebesgue measure on $\mathbb{R}$ with finite variance. We ...
1 vote
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Accuracy of MLE

Hi I have a question related to MLE. Consider a simple linear regression model: y = a + b*x + u Here, if the regressor X has small variability, the OLE estimator could be inaccurate. My question is ...
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Why does MLE tend to normal distribution

We have $X_1,\dots, X_n$ are iid (the distribution can be of any type, e.g. Bernoulli (p), normal ($\mu, \sigma^2$), Poisson ($\lambda$). If we use MLE $\hat \theta$ to estimate any parameter $\theta$ ...
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MLE and consistency and efficiency of MLE

Here is my understanding of Likelihood function, maximum likelihood estimator (MLE) and consistency and efficiency of MLE. (Notes: Comments are not main parts of this post and can be skipped. Only ...
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Vector-valued estimators, intuitively why $var(\widetilde{\beta})-var(\widehat{\beta})$ being p.s.d. means $\widehat{\beta}$ more efficient?

For two scalar unbiased estimators $\widehat{\alpha}$ and $\widetilde{\alpha}$, we know that if one has smaller variance, then we say it is more efficient, which intuitively means that this estimator ...
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In regression modeling, are there any caveats to always using robust standard errors?

Aside from efficiency issues, is there anything else to this?
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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 ...
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Are GAM suitable for inference?

Are the estimators unbiased efficient and consistent? Or is GAM better for classification and prediction than non additive models? Interaction terms aren’t allowed in GAM.
1 vote
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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\...
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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 ...
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In the case of lognormal distribution, when can the median be more efficiently estimated than the mean?

I understand, that in the case of normal distribution, the estimation of the mean (from samples) is more efficient (i.e. of less risk), than the estimation of the median. According e.g. to this post, ...
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