Given a set of samples from a given probability distribution with an unknown parameter , where is the parameter space that is a subset of . Let be an estimator of . Allowing the sample size to vary, we get a sequence of estimators for :
for all .
Remark. Suppose is an estimator of such that the sequence is consistent. If and are two convergent sequences of constants with and , then the sequence , defined by , is consistent, is an estimator of .
First, observe that
As , , , and . So the last expression goes to as . Therefore,
and thus is a consistent sequence of estimators of . ∎
|Date of creation||2013-03-22 15:26:34|
|Last modified on||2013-03-22 15:26:34|
|Last modified by||CWoo (3771)|
|Defines||consistent sequence of estimators|