Definition
Let be an unknown random vector variable, and let be a known random vector variable (the measurement or observation). An estimator of is any function of the measurement . The estimation error vector is given by and its mean squared error (MSE) is given by the trace of error covariance matrix
- ,
where the expectation is taken over both and . When is a scalar variable, then MSE expression simplifies to . Note that MSE could equivalently be defined in other ways, since
The MMSE estimator is then defined as the estimator achieving minimal MSE.
Read more about this topic: Minimum Mean Square Error
Famous quotes containing the word definition:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)