# 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 $\delta$ be an estimator of $\theta$.

The bias of $\delta$ is defined as:

$\map {\operatorname{bias} } \delta = \expect {\map \delta {\mathbf X} } - \theta$