Partial identification in the statistical matching problem.

Area of Science:

• Statistics
• Data Science
• Econometrics

Background:

• Statistical matching integrates disparate datasets, but missing joint variables create unidentifiable models.
• Partially identified models allow statistical inference by bounding parameters instead of precise estimation.
• Bounding parameters in matching problems often requires finding positive-definite completions of partially specified covariance matrices.

Purpose of the Study:

• To address the limitations of existing methods for characterizing covariance matrix completions in high-dimensional statistical matching.
• To propose a novel computational approach for estimating feasible parameter bounds in complex matching scenarios.

Main Methods:

• Development of a Gibbs sampler designed to draw from the set of possible positive-definite completions of a partially specified covariance matrix.
• Application of the Gibbs sampler to high-dimensional statistical matching problems.

Main Results:

• The proposed Gibbs sampler effectively generates samples from the set of possible completions, enabling feasible parameter bounding.
• Variation in observed samples from the Gibbs sampler provides an estimate of the feasible parameter region.
• The method demonstrates scalability and ease of extension to high-dimensional statistical matching challenges.

Conclusions:

• The Gibbs sampler offers a viable solution for bounding parameters in high-dimensional statistical matching problems where traditional methods fail.
• This approach enhances statistical inference capabilities by providing robust parameter estimates in the presence of missing data patterns.
• The developed methodology facilitates the integration and analysis of complex, multi-dataset information.