METHOD OF MOMENTS ESTIMATION: Simple and Complicated Settings

The method of moments (MOM) is used to estimate parameters in the LLd. setup in introductory statistics courses. This method, however, is quickly set aside in favor of the method of maximum likelihood (ML). The main justification for this is the asymptotic efficiency of ML estimates if the assumed model is correct. We will argue that, in some situations, MOM estimates are actually better than ML estimates for small sample sizes even if the assumed model is correct. More importantly, the MOM can be extended in a natural way to very general settings where ML would be intractable, and MOM is a robust alternative to ML when we have insufficient knowledge of the underlying population.