“ …(this paradox) is of fundamental importance in modern statistics, introducing concepts of shrinkage to further reduce the mean squared error, especially in higher dimensional statistics that is particularly relevant nowadays, in the world of machine learning, for example. However, this is usually ignored, because it is mostly seen as a toy problem. Precisely because it is such a simple problem that illustrates the problem of maximum likelihood estimation! This paradox is the subject of many blogposts (linked below), but not really here on YouTube, except in some lecture recordings, so I have to bring this up to YouTube. This is not to say that maximum likelihood estimator is not useful — in most situations, especially in lower dimensional statistics, it is still good, but to hold it to such a high place, as statisticians did before 1961? That is not a healthy attitude to this theory. One thing I did not say, but perhaps a lot of people will want me to, is that this is an emprical Bayes estimator, but again, more links below.”
