  Identifying which variables do influence a response while controlling false
positives pervades statistics and data science. In this paper, we consider a
scenario in which we only have access to summary statistics, such as the values
of marginal empirical correlations between each dependent variable of potential
interest and the response. This situation may arise due to privacy concerns,
e.g., to avoid the release of sensitive genetic information. We extend
GhostKnockoffs (He et al. [2022]) and introduce variable selection methods
based on penalized regression achieving false discovery rate (FDR) control. We
report empirical results in extensive simulation studies, demonstrating
enhanced performance over previous work. We also apply our methods to
genome-wide association studies of Alzheimer's disease, and evidence a
significant improvement in power.
