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?