Definition and Basic Properties
If is a vector of n predictions, and is the vector of the true values, then the MSE of the predictor is:
The MSE of an estimator with respect to the estimated parameter is defined as
The MSE is equal to the sum of the variance and the squared bias of the estimator
The MSE thus assesses the quality of an estimator in terms of its variation and unbiasedness. Note that the MSE is not equivalent to the expected value of the absolute error.
Since MSE is an expectation, it is not a random variable. It may be a function of the unknown parameter, but it does not depend on any random quantities. However, when MSE is computed for a particular estimator of the true value of which is not known, it will be subject to estimation error. In a Bayesian sense, this means that there are cases in which it may be treated as a random variable.
Read more about this topic: Mean Squared Error
Famous quotes containing the words definition, basic and/or properties:
“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)
“The basic Female body comes with the following accessories: garter belt, panti-girdle, crinoline, camisole, bustle, brassiere, stomacher, chemise, virgin zone, spike heels, nose ring, veil, kid gloves, fishnet stockings, fichu, bandeau, Merry Widow, weepers, chokers, barrettes, bangles, beads, lorgnette, feather boa, basic black, compact, Lycra stretch one-piece with modesty panel, designer peignoir, flannel nightie, lace teddy, bed, head.”
—Margaret Atwood (b. 1939)
“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)