Diagnosing and Handling Common Violations of Missing at Random

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Ignorable likelihood (IL) methods are standard for handling missing data in multivariate models under the missing at random (MAR) assumption.
• Violations of MAR, where unobserved variables influence missingness, necessitate advanced techniques.
• Existing data-deletion methods, while effective, require careful selection based on the MAR violation type.

Purpose of the Study:

• To develop diagnostic tests for identifying specific violations of the MAR assumption.
• To propose a test-based estimator that adaptively applies data-deletion strategies.
• To evaluate the performance of the proposed estimator against standard IL approaches.

Main Methods:

• Development of a likelihood-ratio test for heteroscedastic regression models.
• Implementation of a kernel conditional independence test for MAR violation detection.
• Construction of a test-based estimator utilizing these diagnostic tools.

Main Results:

• The proposed diagnostic tests effectively identify MAR violations.
• The test-based estimator demonstrates superior performance over IL methods in severe missing data scenarios.
• The estimator shows comparable performance to IL methods when missing data issues are less pronounced.

Conclusions:

• The developed diagnostic tests and test-based estimator offer a robust solution for handling MAR violations in statistical modeling.
• This approach provides a data-driven method for selecting appropriate missing data handling strategies.
• The findings have significant implications for improving the accuracy and reliability of statistical analyses with incomplete datasets.