Definition:Bias of Estimator

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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

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): unbiased estimator
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): unbiased estimator
• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $8.7$: Unbiased Estimators: Definition $8.7.1$