Properties
- Under some weak regularity assumptions, the MMSE estimator is uniquely defined, and is given by
-
- In other words, the MMSE estimator is the conditional expectation of given the known observed value of the measurements.
- If and are jointly Gaussian, then the MMSE estimator is linear, i.e., it has the form for matrix and constant . As a consequence, to find the MMSE estimator, it is sufficient to find the linear MMSE estimator. Such a situation occurs in the example presented in the next section.
- The orthogonality principle: An estimator is MMSE if and only if
-
- and
- for every affine function of the measurements.
Read more about this topic: Minimum Mean Square Error
Famous quotes containing the word properties:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)