Variance of an estimator (${\mathrm{Var}}_{\theta }(\hat{\theta })$)

The variance of an estimator is the variance of its sampling distribution under the parameter value $\theta$.

The asymptotic variance is the variance appearing in the limiting distribution of a suitably rescaled estimator, commonly $\sqrt{n}({\hat{\theta }}_n-\theta )$.

The bias-variance tradeoff describes how increasing model flexibility commonly decreases systematic approximation bias while increasing sampling variance, or conversely how stronger smoothing decreases variance while increasing bias.