FIGURE 3.

Histograms of the bootstrap samples of the cross-validated improvement measures for $d_0$ random (left column) and $d_0$ best (right column) for the response model of Eq. 12 for different values of n. ${\widehat{I}}_0$ is illustrated with a thick black line. The ${\text{CI}}_{{\mu }_{I_0},95\%}$ computed via the percentile method is illustrated by thin black lines. The true population improvement ${\mu }_{I_0}^{\text{*}}$ given the optimal rule $d^{\text{*}}$ is illustrated with a dotted black line.