Bias of an estimator
Topic of Estimation, part of Statistical inference
Bias of an estimator
| Type | Topic |
| Taught in | Estimation |
| Part | Statistical inference |
| Questions using it | 1 |
\operatorname{bias}(\hat\theta)=\mathbb{E}\hat\theta-\theta, the average amount by which an estimator misses its target. An estimator with zero bias is unbiased. The mean squared error is the variance plus the squared bias, so a small bias can be worth accepting for a larger drop in variance.
In Estimation
From Estimation
The split is the variance–bias tradeoff. Removing a bias often raises the variance, and sometimes by more than the squared bias that was removed. An estimator with a small bias can then have a smaller mean squared error than an unbiased competitor. One estimator is more efficient than another when its mean squared error is no larger at every parameter value, and smaller at some.
Used in
- Taught in Estimation
- Questions that use it (1) — Clustering and smoothing choices (answer)
- All 5 questions on Estimation
See also
Estimator · Unbiased estimator · Mean squared error · Variance · Method of moments · Sample correlation coefficient · Likelihood function · Maximum likelihood