Unbiased Estimator

probability-theory

Definition

Unbiased Estimator

Let $\theta$ be a parameter of a model, and let $\hat{\theta }=T(X_1,\dots ,X_n)$ be an estimator (a random variable depending on the sample).

The estimator $\hat{\theta }=\hat{\theta }(\mathbf{X})$ is called unbiased for $\theta$ if its expectation equals the true parameter:

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

Equivalently: on average (over repeated samples from the model), the estimator neither systematically overestimates nor underestimates $\theta$.