A Distributed and Integrated Method of Moments for High-Dimensional Correlated Data Analysis

Abstract

This article is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multilevel nested correlations. We develop a divide-and-conquer procedure implemented in a fully distributed and parallelized computational scheme for statistical estimation and inference of regression parameters. Despite significant efforts in the literature, the computational bottleneck associated with high-dimensional likelihoods prevents the scalability of existing methods. The proposed method addresses this challenge by dividing responses into subvectors to be analyzed separately and in parallel on a distributed platform using pairwise composite likelihood. Theoretical challenges related to combining results from dependent data are overcome in a statistically efficient way using a meta-estimator derived from Hansen’s generalized method of moments. We provide a rigorous theoretical framework for efficient estimation, inference, and goodness-of-fit tests. We develop an R package for ease of implementation. We illustrate our method’s performance with simulations and the analysis of the EEG data, and find that iron deficiency is significantly associated with two auditory recognition memory related potentials in the left parietal-occipital region of the brain. Supplementary materials for this article are available online.

Keywords:

• Composite likelihood
• Divide-and-conquer
• Generalized method of moments
• Parallel computing
• Scalable computing

Supplementary Materials

Additional technical details, proofs of theorems, simulations and data analysis results are in the supplementary materials, along with an R package.

Acknowledgments

The authors are grateful for the constructive comments given by the associate editor and the anonymous reviewers that led to a significant improvement of the article.

Additional information

Funding

This research was funded by grants NSF DMS1811734, NIH R01ES024732, and NIH P01ES022844.