Mean Squared Error - Definition and Basic Properties

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:

    The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.
    William James (1842–1910)

    I fly in dreams, I know it is my privilege, I do not recall a single situation in dreams when I was unable to fly. To execute every sort of curve and angle with a light impulse, a flying mathematics—that is so distinct a happiness that it has permanently suffused my basic sense of happiness.
    Friedrich Nietzsche (1844–1900)

    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)