Unbiased Estimator

probability-theory

Definition

Unbiased Estimator

Let $\theta$ be a parameter of a distribution and $\hat{\theta }=T(X_1,\dots ,X_n)$ an estimator built from a random sample. The estimator is unbiased for $\theta$ when its expectation equals the true parameter:

$$\mathbb{E}[\hat{\theta }]=\theta ,$$

equivalently when its bias is zero. Over repeated samples drawn from the same distribution, an unbiased estimator neither systematically overestimates nor underestimates $\theta$; it is correct on average.