Fig. 9.

Simulation for a non-Gaussian design. The $j$th feature takes values in $\left\{\mathrm{0,1,2}\right\}$ with probabilities $p_j^2,2p_j\left(1-p_j\right),{\left(1-p_j\right)}^2$; here, $p_j\in \left[0.25,0.75\right]$ and $p_j\hspace{0.17em}\ne \hspace{0.17em}{p}_k$ for $j\hspace{0.17em}\ne \hspace{0.17em}k$. Features are then centered and rescaled to have unit variance. The setting is otherwise the same as for Fig. 3. (A) Analogue of Fig. 3A. Red line has slope ${\alpha }_{\star }\approx 1.499$. (B) Analogue of Fig. 6B. Observe the same behavior as earlier: The theory predicts correctly the bias and the decorrelation between the bias-adjusted residuals and the true effect sizes.