Penalized Exponentially Tilted Likelihood for Growing Dimensional Models with Missing Data

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Missing data in high-dimensional models presents estimation and variable selection challenges.
• Existing methods may lack consistency or robustness when dealing with randomly missing responses.
• Accurate statistical inference is crucial for complex datasets in various scientific fields.

Purpose of the Study:

• To develop a novel penalized exponentially tilted (ET) likelihood approach for simultaneous parameter estimation and variable selection.
• To address the issue of missing response data in growing dimensional models using inverse probability weighting.
• To establish robust statistical properties and hypothesis testing capabilities for the proposed methodology.

Main Methods:

• Development of a penalized exponentially tilted (ET) likelihood function.
• Application of the inverse probability weighted (IPW) approach to handle missing response data.
• Construction of an ET likelihood ratio statistic for hypothesis testing on parameters.
• Theoretical analysis of consistency, asymptotic properties, and oracle properties of estimators.

Main Results:

• The proposed penalized ET likelihood method enables simultaneous parameter estimation and variable selection.
• Inverse probability weighting ensures the consistency of parameter estimators despite missing data.
• The ET likelihood ratio statistic demonstrates Wilks' property for hypothesis testing.
• Theoretical properties including consistency and oracle properties are established under specific conditions.

Conclusions:

• The penalized ET likelihood offers a powerful tool for high-dimensional statistical modeling with missing data.
• The methodology provides reliable parameter estimation and variable selection, enhancing statistical inference.
• The approach is validated through simulations and practical application to thyroid data, demonstrating its effectiveness.