mean squared error

Note that other distortion measures can also be considered, although mean squared error is a popular one.

Mean squared errors are also indicated in the plots.

However, we can achieve a lower mean squared error using a biased estimator.

Other loss functions can be conceived, although the mean squared error is the most widely used and validated.

Like variance, mean squared error has the disadvantage of heavily weighting outliers.

There are, however, some scenarios where mean squared error can serve as a good approximation to a loss function occurring naturally in an application.

This estimator also has a uniformly smaller mean squared error than the corrected sample standard deviation.

Surprisingly, it turns out that the "ordinary" estimator proposed above is suboptimal in terms of mean squared error.

However, a terminological difference arises in the expression mean squared error (MSE).

When we use the mean squared error as distortion measure, we have (for amplitude-continuous signals):

In the end the FIC selects the model with smallest estimated mean squared error.

Criticism The use of mean squared error without question has been criticized by the decision theorist James Berger.

The most common choice of the loss function is quadratic, resulting in the mean squared error criterion of optimality.

If a prior probability on is known, then a Bayes estimator can be used to minimize the mean squared error, .

More accurately, one would like to minimize the mean squared error (MSE) between and .

As a result, there was considerable shock and disbelief when Stein demonstrated that, in terms of mean squared error , this approach is suboptimal.

Specifically, it is possible to furnish estimators that improve considerably upon the maximum likelihood estimate in terms of mean squared error.

As we're restricting to unbiased estimators, minimum mean squared error implies minimum variance.

In fact, if we use mean squared error as a selection criterion, many biased estimators will slightly outperform the "best" unbiased ones.

In other words, in the setting discussed here, there exist alternative estimators which always achieve lower mean squared error, no matter what the value of is.

(It follows that the sample mean is also the best single predictor in the sense of having the lowest root mean squared error.)

This latter formula serves as an unbiased estimate of the variance of the unobserved errors, and is called the mean squared error.

In some cases, an estimator with a small bias may have lesser mean squared error or be median-unbiased (rather than mean-unbiased, the standard unbiasedness property).

However it can be shown that the biased estimator is "better" than the s in terms of the mean squared error (MSE) criterion.

The mean squared error of an estimator is the expected value of the square of its deviation from the unobservable quantity being estimated.