Identification and Estimation of Nonlinear Models Using Two Samples with Nonclassical Measurement Errors.

Area of Science:

• Econometrics
• Statistical Modeling
• Biostatistics

Background:

• Errors-in-Variables (EIV) models are common in various scientific fields.
• Traditional methods often require strong assumptions about measurement error distributions.
• Existing techniques may struggle with nonclassical errors or limited sample data.

Purpose of the Study:

• To develop a method for identifying and estimating general nonlinear EIV models using two samples.
• To address situations with unknown and potentially correlated measurement errors.
• To provide a robust framework for statistical inference in complex EIV settings.

Main Methods:

• Utilizing two distinct samples with shared regression but varying covariate distributions.
• Employing nonparametric identification strategies without instrumental variables.
• Proposing sieve Quasi Maximum Likelihood Estimation (Q-MLE) for parameterized models.
• Establishing theoretical properties like root-n consistency and asymptotic normality.

Main Results:

• Demonstrated nonparametric identification of the general latent nonlinear EIV model under nonclassical errors.
• Established root-n consistency and asymptotic normality for the proposed Q-MLE.
• Showcased semiparametric efficiency under correct model specification.
• Validated the method through Monte Carlo simulations and a real-world data application.

Conclusions:

• The proposed two-sample approach effectively handles general nonlinear EIV models with nonclassical measurement errors.
• Sieve Q-MLE provides a statistically sound and efficient estimation method.
• The methodology offers a powerful tool for empirical research across disciplines facing EIV challenges.