The article discusses different econometric models and methods for identifying and estimating parameters in these models. It focuses on transformation models with unknown transformations and finite identification in parametric models. The researchers introduce new conditions for identification, develop an extremum estimator, and study the properties of maximum likelihood estimators under finite identification. They also explore nonparametric tests for density ratio ordering between probability distributions. Key findings include the development of a sieve extremum estimator, the use of bootstrap for inference in finitely identified models, and the derivation of limit distributions for nonparametric tests of density ratio ordering.