Estimating Large Correlation Matrices for International Migration.

Area of Science:

• Demography
• Statistics
• International Relations

Background:

• Probabilistic population projections are crucial for global planning.
• International migration data is complex and challenging to model accurately.
• Existing methods struggle with estimating correlation matrices from limited data.

Purpose of the Study:

• To develop a robust statistical estimator for correlation matrices in population projections.
• To address the challenge of estimating large correlation matrices with sparse data.
• To improve the accuracy and reliability of international migration forecasts.

Main Methods:

• Proposed a maximum a posteriori (MAP) estimator for correlation matrices.
• Introduced an interpretable informative prior distribution for regularization.
• Applied the estimator to United Nations population projection data.
• Conducted a simulation study to compare performance against existing methods.

Main Results:

• The proposed MAP estimator significantly reduces spurious correlations.
• Estimated correlation structure improved net migration projections for regional aggregates.
• Demonstrated narrower migration projections for Africa and wider for Europe.
• Simulation results showed superior performance compared to Pearson correlations and simple shrinkage.

Conclusions:

• The novel MAP estimator offers a more reliable method for modeling international migration.
• Improved correlation matrix estimation leads to more accurate population projections.
• This approach enhances the forecasting capabilities for regional demographic trends.