Standard Error

Let

The standard error of the estimator refers to its standard deviation, i.e.,

Notes:

• The standard error is a measure of variability of the probability distribution of an estimator. It is also equal to the standard deviation of the error distribution since
  
  
  
• As an example, the standard error of the sample mean derived from a random sample is
  
  
  The standard error for a difference of two sample means derived from independent random samples of size m and n is
  
  
  
• The figure below shows the probability densities for the errors associated with three different unbiased estimators. Here, the error distribution with the smallest (largest) spread corresponds to the estimator with the smallest (largest) standard error.
  
  
• An unbiased estimator with small standard error is desirable since such estimators have a relatively low probability of making large errors. In other words, such estimators have a high probability of being "on target".