0
$\begingroup$

I am studying statistical inference. I want to know what should be the general strategy for proving the consistency of an estimator.

In most problems whenever I prove consistency, I usually see whether the estimator is a function of the maximum likelihood estimator (MLE). I have seen in Casella and Berger's text that MLE estimator are consistent in most cases. And also, functions of MLE estimators are also MLE. I just wanted to know whether my approach to proving the consistency is right. If not, can you suggest some ways by which I can approach proofs of consistency?

$\endgroup$
2
$\begingroup$

I think there are a number of approaches. Other than MLE-related approaches, two that I happen to have used are:

  • Consistency is preserved under a continuous transformation. See Casella-Berger pp. 233 Theorem 5.5.4.
  • Asymptotic normality implies consistency. See Casella-Berger pp. 472-473 Example 10.1.13.

I'd be interested to hear other approaches from the community!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.