Definition
(Bias). Let \(\hat\theta\) be an estimator. The bias of \(\hat\theta\) is defined to be
\begin{align*} B(\hat \theta) = \mathbb E[\hat \theta] - \theta. \end{align*}If \(B(\hat\theta) = 0\) then \(\hat \theta\) is said to be unbiased, otherwise it is biased.