Which term describes an estimator that systematically overestimates or underestimates the parameter?

Which term describes an estimator that systematically overestimates or underestimates the parameter?

• A. Unbiased
• B. Biased
• C. Consistent
• D. Inconsistent

Answer: (B)

The concept being tested is bias in an estimator. An estimator is biased when its expected value across repeated samples does not equal the true parameter, meaning it tends to overshoot or undershoot the parameter on average. This is a persistent, directional error, not something that cancels out with more data. By contrast, an unbiased estimator has an average of its estimates equal to the parameter, so there’s no systematic over- or underestimation. Consistency is about how the estimator behaves as sample size grows: a consistent estimator produces values that get arbitrarily close to the parameter with more data, which is different from whether it tends to over- or under-estimate in finite samples. Inconsistent means it fails to approach the parameter as sample size increases.

The concept being tested is bias in an estimator. An estimator is biased when its expected value across repeated samples does not equal the true parameter, meaning it tends to overshoot or undershoot the parameter on average. This is a persistent, directional error, not something that cancels out with more data. By contrast, an unbiased estimator has an average of its estimates equal to the parameter, so there’s no systematic over- or underestimation. Consistency is about how the estimator behaves as sample size grows: a consistent estimator produces values that get arbitrarily close to the parameter with more data, which is different from whether it tends to over- or under-estimate in finite samples. Inconsistent means it fails to approach the parameter as sample size increases.