The rates at which the
proposed procedure ranks G1, . . . , G4 top 4 are 0.69, 0.50, 0.91 and 0.79 respectively. Similar to the outcomes in Table 4,
these results are close to those of KSIR for G3 and G4, which have rates 0.90 and 0.81, while they are lower to those of
KSIR for G1 and G2, where KSIR obtains rates 0.78 and 0.77. In the second scenario we generated 10 groups with 150
covariates each, where the response only depends on the first group through Y = exp(G1) + ε. The group G1 in this case
is generated in the following way G1 = X11 + · · · + X16 − X17 − · · · − X110 + Xi1
+ Xi2
+ Xi3+ Xi4
, where the last 4
terms are interactions randomly selected from all two-way interactions of the first 10 predictors without replacement. The
proposed procedure ranked G1 as the top group 83% of the time, slightly higher rate compared to that of KSIR-GAM, which
achieves 81%.