We demonstrate how the HI analysis can be applied to sub-GeV DM scattering off electrons for noble gas targets such as Xe and
semiconductor targets such as Ge and Si. In the HI analysis method, properties of the local DM halo velocity distribution are inferred from direct DM detection data, which allows the comparison of different data sets without making any assumption on the uncertain local dark halo characteristics. This method had previously been developed for and applied only to DM scattering off nuclei. We additionally show that in-medium effects could significantly affect HI analysis results for semiconductor targets Ge and Si and thus are essential for proper inference of local DM halo characteristics from direct DM detection data.