Definition:Bias of Estimator
In particular: statistical model.
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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:
- $\map {\operatorname{bias} } \delta = \expect {\map \delta {\mathbf X} } - \theta$
Sources
- 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $8.7$: Unbiased Estimators: Definition $8.7.1$
