My Monday post called for a classification of estimation and testing methods according to an exhaustive set of performance criteria. I thought a little about it in the last few days, and the following features of statistical analysis may help to make such a classification viable:
1. The sum of independent identically distributed variables tends to a normal distribution. This result is the Central Limit Theorem, and applies to more general sets of variables and random series.
2. Most estimation methods can be represented by the Generalized Method of Moments.
3. There are maybe half a dozen genuinely different ideas in mainstream econometrics, like minimisation of the expectation-observation gap, looking at patterns of residuals, and spectral analysis.
So the complete classification could be based on the limited number of combinations of these different features. The founding GMM proofs, which combine generalised estimation methods with asymptotic analysis of normally converged variables, are a step towards the goal - I have praised the GMM in past posts.