Bias (Estimator)

The bias of an Estimator $\tilde\theta$ is defined as

$$B(\tilde\theta) \equiv \left\langle{\tilde\theta}\right\rangle{}-\theta.$$

It is therefore true that

$$\tilde\theta-\theta = (\tilde\theta-\langle\tilde\theta\rang... ... = (\tilde\theta-\langle\tilde\theta\rangle)+B(\tilde\theta).$$

An Estimator for which $B = 0$ is said to be Unbiased.

See also Estimator, Unbiased