The Annals of Applied Statistics

Estimating large correlation matrices for international migration

Jonathan J. Azose and Adrian E. Raftery

Full-text: Open access

Abstract

The United Nations is the major organization producing and regularly updating probabilistic population projections for all countries. International migration is a critical component of such projections, and between-country correlations are important for forecasts of regional aggregates. However, in the data we consider there are 200 countries and only 12 data points, each one corresponding to a five-year time period. Thus a $200\times200$ correlation matrix must be estimated on the basis of 12 data points. Using Pearson correlations produces many spurious correlations. We propose a maximum a posteriori estimator for the correlation matrix with an interpretable informative prior distribution. The prior serves to regularize the correlation matrix, shrinking a priori untrustworthy elements towards zero. Our estimated correlation structure improves projections of net migration for regional aggregates, producing narrower projections of migration for Africa as a whole and wider projections for Europe. A simulation study confirms that our estimator outperforms both the Pearson correlation matrix and a simple shrinkage estimator when estimating a sparse correlation matrix.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 2 (2018), 940-970.

Dates
Received: November 2017
Revised: April 2018
First available in Project Euclid: 28 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1532743482

Digital Object Identifier
doi:10.1214/18-AOAS1175

Keywords
Correlation estimation international migration maximum a posteriori estimation high-dimension

Citation

Azose, Jonathan J.; Raftery, Adrian E. Estimating large correlation matrices for international migration. Ann. Appl. Stat. 12 (2018), no. 2, 940--970. doi:10.1214/18-AOAS1175. https://projecteuclid.org/euclid.aoas/1532743482


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