A Bayesian Interpretation of Extremim Estimators
Extremum estimation is typically an ad hoc semi-parametric estimation procedure which is only justified on the basis of the asymptotic properties of the estimators. For a fixed finite data set, consider a large number of investigations using different extremum estimators to estimate the same parameter vector. The resulting empirical distribution of point estimates can be shown to coincide with a Bayesian posterior measure on the parameter space induced by a minimum information procedure. The Bayesian interpretation serves a number of purposes ranging from lending legitimacy to the use of those procedures in small sample problems, to helping prove asymptotic properties by reference to Bayes central limit theorems, to laying a foundation for combining point estimates from various extremum estimation experiments for statistical decision processes.
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- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Zellner, A., 1988. "Optimal Information-Processing And Bayes' Theorem," Papers m8803, Southern California - Department of Economics.
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