Definition:Bias of Estimator

Definition
Let $\theta$ be a population parameter of some statistical model.

Let $\mathbf X$ be a random sample from this population.

Let $\hat \theta \left({\mathbf X}\right)$ be an estimator of $\theta$ given $\mathbf X$.

The bias of $\hat \theta$ is defined as:


 * $\operatorname{bias} \left({\hat \theta}\right) = \mathbb E \left[{\hat \theta \left({\mathbf X}\right)}\right] - \theta$

An estimator with zero bias is referred to as an unbiased estimator.