Is it ever possible for the limit of the MSE of an estimator be infinity?
I was doing an exercise and it turns out that the estimator is consistent but the limit of the MSE is infinity, so I am wondering if this result makes sense or did I make a mistake somewhere. I do know that just because the estimator is consistent, that does not mean that the limit of its MSE must be 0. But I did not expect that the limit of an MSE can ever be infinity. If this is true, then what is the interpretation of this kind of estimator?