Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint...

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Missing data present significant challenges in statistical analysis, particularly when missingness is non-ignorable.
• Accurate inference about mean functionals requires robust methods to handle complex missing data mechanisms.

Purpose of the Study:

• To develop a method for the identification and inference of mean functionals in the presence of non-ignorable missing outcome data.
• To establish conditions for the identifiability and estimability of mean functionals using a shadow variable approach.

Main Methods:

• Leveraging a shadow variable to derive a necessary and sufficient condition for the identification of mean functionals.
• Characterizing a necessary condition for $$-estimability involving a representer equation.
• Developing a consistent estimator for the solution set and adapting extremum estimator theory for non-parametric estimation.

Main Results:

• A condition for identification is established, applicable even when the full data distribution is not identified.
• A novel, asymptotically normal, and locally efficient estimator is constructed, achieving the semi-parametric efficiency bound.
• The method's efficacy is demonstrated through simulations and a real-world application in home pricing.

Conclusions:

• The proposed shadow variable method provides a powerful framework for addressing non-ignorable missing data in mean functional analysis.
• The developed estimator offers a statistically sound and efficient solution for complex missing data problems.
• This approach has broad applicability in various fields requiring robust statistical inference from incomplete datasets.