efficient estimator

In this case, pooling observations across countries is an efficient estimator.

Despite its simplicity, the trimean is a remarkably efficient estimator of population mean.

Thus, the sample mean is a finite-sample efficient estimator for the mean of the normal distribution.

Objective: The primary goal is to obtain an efficient estimator for the parameter , based on the data.

Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance.

Finite-sample efficient estimators are extremely rare.

Efficient estimators are always minimum variance unbiased estimators.

Mean squared error is used for obtaining efficient estimators, a widely used class of estimators.

"Efficient estimators for the Good Family" : Commun.

Thus an efficient estimator need not exist, but if it does, it is the MVUE.

In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some "best possible" manner.

Despite its simplicity, for estimating the standard deviation of a normal distribution, the scaled interdecile range gives a reasonably efficient estimator.

For some estimators, they can attain efficiency asymptotically and are thus called asymptotically efficient estimators.

When this requirement is violated this is called heteroscedasticity, in such case a more efficient estimator would be weighted least squares.

Thus in that case, the corresponding would be a more efficient estimator of compared to , based on using the mean squared error as the performance criteria.

An efficient estimator is also the minimum variance unbiased estimator (MVUE).

Obtaining consistent and efficient estimators for the regression parameters in the linear model with asymmetrical and longitudinally correlated errors is, however, proven to be difficult.

Hausman also showed that the covariance between an efficient estimator and the difference of an efficient and inefficient estimator is zero.

It is also an efficient estimator, i.e. its estimation variance achieves the Cramér-Rao lower bound (CRLB).

This consideration was exploited to provide an efficient estimator of the mean timber volume on the current occasion when sampling with partial replacement (SPR) on two occasions.

However, with clean data or in theoretical settings, they can sometimes prove very good estimators, particularly for platykurtic distributions, where for small data sets the mid-range is the most efficient estimator.

In other words, the sample mean is the (necessarily unique) efficient estimator, and thus also the minimum variance unbiased estimator (MVUE), in addition to being the maximum likelihood estimator.

We say that the estimator is finite-sample efficient estimator (in the class of unbiased estimators) if it reaches the lower bound in the Cramér-Rao inequality above, for all θ Θ.

This is because an efficient estimator maintains equality on the Cramér-Rao inequality for all parameter values, which means it attains the minimum variance for all parameters (the definition of the MVUE).

However, it finds some use in special cases: it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid-ranges address robustness, and as an L-estimator, it is simple to understand and compute.