Bias
Bias, in estimation, is the systematic gap between an estimator's expected value and the true population parameter.
Also known asestimator bias
See it move
A two-column comparison contrasts an unbiased estimator, where the expected value E[θ̂] equals the true parameter θ and the bias is zero, with a biased estimator, where E[θ̂] differs from θ by a non-zero amount and estimates land systematically off-centre. The comparison notes that omitted variable bias — leaving a relevant correlated regressor out of a regression model — is the most common source of such systematic error.
The formula
Variables
- Estimator
- Expected value of the estimator across all possible samples
- True population parameter
An unbiased estimator has E(θ̂) = θ, making the bias exactly zero.
Check yourself
An estimator of the population mean consistently overestimates the true value by exactly €120, regardless of which sample is drawn. Which statement correctly characterises this estimator?