Procedure 2.

Selecting lambdas under the assumption of independence: equal groups sizes

input: q ∈ (0, 1), w > 0, p, n, m, l ∈ ℕ

${\lambda }_1:=\frac{1}{w}{F}_{{\chi }_l}^{-1}(1-\frac{q}{m})$;

For i ∈ {2, . . . , m}:

λS := (λ1, . . . , λi−1)⊤;

$\mathcal{S}:=\sqrt{\frac{n-l(i-1)}{n}+\frac{w^2{\Vert {\lambda }^S\Vert }_2^2}{n-l(i-1)-1}}$;

${\lambda }_i^{\ast }:=\frac{\mathcal{S}}{w}{F}_{{\chi }_l}^{-1}(1-\frac{q·i}{m})$;

if ${\lambda }_i^{\ast }\le {\lambda }_{i-1}$, then put ${\lambda }_i:={\lambda }_i^{\ast }$. Otherwise, stop the procedure and put λj := λi−1 for j ≥ i;

end for