REMI: REGRESSION WITH MARGINAL INFORMATION AND ITS APPLICATION IN GENOME-WIDE ASSOCIATION STUDIES

In this study, we consider the problem of variable selection and estimation in high-dimensional linear regression models when complete data are not accessible, but only certain marginal information or summary statistics available. This is motivated from Genome-wide association studies (GWAS) that have been widely used to identify risk variants underlying complex human traits/diseases. With a large number completed GWAS, statistical methods using become more important because restricted accessibility individual-level sets. Theoretically guaranteed highly demanding advance inference with amount available information. Here propose an $\ell_1$ penalized approach, REMI, estimate high dimensional coefficients external reference samples. We establish upper bound on error REMI estimator, which has same order as minimax Lasso data. particular, obtained samples together small samples, yields good prediction results, outperforms sample size accessible can be limited. Through simulation real analysis NFBC1966 GWAS set, demonstrate applicable. The developed R package codes reproduce all results at https URL