Estimation Error

Let

Then, the estimation error associated with the point estimator is

Notes:

• The quality of a point estimator is determined by its correponding estimation error. More precisely, statistical properties of the estimation error like its E(e) and E(e²) tell us how good a point estimator is since they determine the bias and mean squared error of the estimator.
• As an example, if we use the sample mean to estimate the population mean, the estimation error is
  
  
  Also, if we use the sample variance to estimate the population variance, the estimation error is
• The above definition is not restriced to scalar (i.e., one-dimensional) parameters only. It is also applicable when considering the estimation error associated with point estimators of any scalar estimand (such as a difference of two means or a ratio of two variances etc.). Indeed, one can also consider extensions to multidimensional estimands.