Domain selection for the varying coefficient model via local polynomial regression.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Varying coefficient models allow predictor-response relationships to change over a domain.
• Identifying regions where predictors are active is crucial for accurate modeling.

Purpose of the Study:

• To develop a statistical framework for identifying the domain of non-zero coefficients in varying coefficient models.
• To incorporate local polynomial smoothing and penalized regression for enhanced model performance.

Main Methods:

• A novel penalized regression approach is proposed, integrating local polynomial smoothing.
• Asymptotic properties of the penalized estimators are derived, demonstrating oracle properties.
• Discussions on bandwidth selection and computational algorithms are included.

Main Results:

• The proposed penalized estimators exhibit desirable statistical properties, mirroring those of local polynomial estimators with known sparsity.
• The method effectively identifies regions where predictors influence the response.
• Simulations and a real data example validate the approach.

Conclusions:

• The penalized varying coefficient model provides an effective tool for domain identification and coefficient estimation.
• The method offers a robust approach for analyzing complex relationships in data.
• This framework enhances the interpretability and accuracy of varying coefficient models.