mean square error
If is an unbiased estimator, then its mean square error is identical to its variance: . An unbiased estimator such that is a minimum value among all unbiased estimators for is called a minimum variance unbiased estimator, abbreviated MVUE, or uniformly minimum variance unbiased estimator, abbreviated UMVU estimator.
Example. Suppose are iid random variables ( independent measurements of the radius of a coin, etc…) from a normal distribution (for example, would be the true radius of the coin, and would be the error component of the measurements). Suppose () is the sample mean. Then is an unbiased estimator, so that
Remark. The square root of MSE is called the “root mean square error”, or rms error for short.
|Title||mean square error|
|Date of creation||2013-03-22 12:07:42|
|Last modified on||2013-03-22 12:07:42|
|Last modified by||CWoo (3771)|
|Synonym||uniformly minimum variance unbiased|
|Defines||minimum variance unbiased estimator|
|Defines||root mean square|