Rejoinder on: Hierarchical inference for genome-wide association studies: a view on methodology with software

We provide a view on high-dimensional statistical inference for genome-wide association studies. It is in part a review but covers also new developments for meta analysis with multiple studies and novel software in terms of an R-package hierinf. Inference and assessment of significance is based on very high-dimensional multivariate (generalized) linear models: in contrast to often used marginal approaches, this provides a step towards more causal-oriented inference.