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.
ψ ( θ )
based on a sample of size
− ψ ( θ + h
where the convergence is in distribution under the law of
is some asymptotic distribution (usually this is a normal distribution with mean zero and variance which may depend on
Both the Hodges' estimator[1] and the James-Stein estimator[2] are non-regular estimators when the population parameter