Divergence and Model Adequacy, a Semiparametric Case Study

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Estimation methods require well-posed problems and consistent estimators.
• Divergence-based inference is applicable to smooth semiparametric models.
• Classical parametric inference has limitations with nuisance parameters.

Purpose of the Study:

• To define adequacy for estimation in divergence-based inference for smooth semiparametric models.
• To investigate conditions for well-posedness and consistent estimation.
• To extend parametric inference to handle nuisance parameters within this framework.

Main Methods:

• Applying divergence-based inference to smooth semiparametric models.
• Analyzing conditions for analytical and statistical adequacy.
• Exploring the choice of divergence, including power divergences.
• Extending inference to parameters of interest and nuisance parameters.

Main Results:

• Established conditions for adequate estimation using divergence-based methods.
• Demonstrated the applicability of power divergences for smooth semiparametric models.
• Showcased the extension of inference to nuisance parameters.
• A simulation study validated the proposed methodology.

Conclusions:

• Divergence-based inference provides a robust framework for smooth semiparametric models.
• Power divergences offer a flexible choice for various estimation tasks.
• The method effectively handles both parameters of interest and nuisance parameters.