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.[1]
An estimator of based on a sample of size is said to be regular if for every :[1]
where the convergence is in distribution under the law of .
Both the Hodges' estimator[1] and the James-Stein estimator[2] are non-regular estimators when the population parameter is exactly 0.