Algorithm 1.

Algorithm for TPC variable selection.

Step 1: Set m = 1 and 𝒮 = ∅, obtain the marginally estimated active set by $${\widehat{\mathcal{A}}}^{[1]}=\{j=1,\cdots ,p:\mid \widehat{\rho }(y,x_j)\mid >T(\alpha ,n,\widehat{\kappa },0)\}.$$

Step 2: Based on 𝒜̂[m−1], construct the mth step estimated active set by $${\widehat{\mathcal{A}}}^{[m]}=\{j\in {\widehat{\mathcal{A}}}^{[m-1]}:\mid \widehat{\rho }(y,x_j\mid x_{\mathcal{S}})\mid >T(\alpha ,n,\widehat{\kappa },\mid \mathcal{S}\mid ),\forall \mathcal{S}\subseteq {\widehat{\mathcal{A}}}^{[m-1]}\backslash \{j\},\mid \mathcal{S}\mid =m-1\}.$$

Step 3: Repeat Step 2 until m = m̂reach.