Figure 2.

The left and center diagrams illustrate two examples of the desired variable selection patterns for overlapping strata. The two gray-highlighted groups in the leftmost diagrams represent the types of selection patterns of interest. Specifically, the two highlighted patterns on the left are elements in 𝒵^C, where the corresponding group structure 𝒢 is defined in equation (4). The diagram on the right illustrates the selection properties when the group structure is misspecified. The groups with white text (HPD, HP, and P) form a true nonzero pattern which violates the structure imposed by our proposed penalty. The gray highlighted color indicates the nonzero pattern which will be selected asymptotically by our estimator with the incorrect group structure.