mean square error
The mean square error of an estimator of aparameter in a statistical model is defined as:
From the definition of the variance,we can express the mean square error in terms of the bias byexpanding the right hand side above:
If is an unbiased estimator, then its mean squareerror is identical to its variance:.An unbiased estimator such that is a minimum value among all unbiased estimators for iscalled a minimum variance unbiased estimator, abbreviated MVUE, or uniformly minimum variance unbiased estimator, abbreviated UMVU estimator.
Example. Suppose are iid randomvariables ( 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 bethe error component of the measurements). Suppose () is the sample mean
. Then is anunbiased 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 |
Canonical name | MeanSquareError |
Date of creation | 2013-03-22 12:07:42 |
Last modified on | 2013-03-22 12:07:42 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 11 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 62J10 |
Classification | msc 94A12 |
Synonym | MSE |
Synonym | MVUE |
Synonym | UMVU |
Synonym | UMVUE |
Synonym | uniformly minimum variance unbiased |
Related topic | MeanSquareDeviation |
Defines | minimum variance unbiased estimator |
Defines | rms error |
Defines | root-mean-square |
Defines | root mean square |
Defines | rms |