Regular estimator

Regular estimators are a class of statistical estimators that satisfy certain regularity conditions which make them amenable to asymptotic analysis. The convergence of a regular estimator's distribution is, in a sense, locally uniform. This is often considered desirable and leads to the convenient property that a small change in the parameter does not dramatically change the distribution of the estimator.

Definition
An estimator $$ \hat{\theta}_n $$ of $$\psi(\theta)$$ based on a sample of size $$n$$ is said to be regular if for every $$h$$:

$$ \sqrt n \left ( \hat{\theta}_n - \psi (\theta + h/\sqrt n) \right ) \stackrel{\theta+h/\sqrt n} {\rightarrow} L_\theta$$

where the convergence is in distribution under the law of $$ \theta + h/\sqrt n$$.

Examples of non-regular estimators
Both the Hodges' estimator and the James-Stein estimator are non-regular estimators when the population parameter $$\theta$$ is exactly 0.