Relative Efficiency
If and are estimators for the parameter, then is said to dominate if:
- its mean squared error (MSE) is smaller for at least some value of
- the MSE does not exceed that of for any value of θ.
Formally, dominates if
holds for all, with strict inequality holding somewhere.
The relative efficiency is defined as
Although is in general a function of, in many cases the dependence drops out; if this is so, being greater than one would indicate that is preferable, whatever the true value of .
Read more about this topic: Efficient Estimator
Famous quotes containing the words relative and/or efficiency:
“Excellence or virtue is a settled disposition of the mind that determines our choice of actions and emotions and consists essentially in observing the mean relative to us ... a mean between two vices, that which depends on excess and that which depends on defect.”
—Aristotle (384323 B.C.)
“Nothing comes to pass in nature, which can be set down to a flaw therein; for nature is always the same and everywhere one and the same in her efficiency and power of action; that is, natures laws and ordinances whereby all things come to pass and change from one form to another, are everywhere and always; so that there should be one and the same method of understanding the nature of all things whatsoever, namely, through natures universal laws and rules.”
—Baruch (Benedict)