Superconsistent estimation and inference in structural econometric models using extreme order statistics

Data-generating processes whose distributions’ supports depend on unknown parameters arise naturally in empirical applications. In such situations the maximum-likelihood estimator is often difficult to calculate and usually has a nonstandard limiting distribution that depends on nuisance parameters. We propose an alternative estimation strategy that is typically simpler to implement than the likelihood approach and allows one to conduct inference using simulation methods. Our proposed estimators are based on the analog estimation principle and bear a striking resemblance to generalized method-of-moments estimators, although here the estimators are generally parameter consistent at rate T rather than the usual rate T.