  The Model-X knockoffs is a practical methodology for variable selection,
which stands out from other selection strategies since it allows for the
control of the false discovery rate (FDR), relying on finite-sample guarantees.
In this article, we propose a Truncated D-vine Copula Knockoffs (TDCK)
algorithm for sampling approximate knockoffs from complex multivariate
distributions. Our algorithm enhances and improves features of previous
attempts to sample knockoffs under the multivariate setting, with the three
main contributions being: 1) the truncation of the D-vine copula, which reduces
the dependence between the original variables and their corresponding
knockoffs, improving the statistical power; 2) the employment of a
straightforward non-parametric formulation for marginal transformations,
eliminating the need for a specific parametric family or a kernel density
estimator; 3) the use of the "rvinecopulib'' R package offers better
flexibility than the existing fitting vine copula knockoff methods. To
eliminate the randomness in distinct realizations resulting in different sets
of selected variables, we wrap the TDCK method with an existing derandomizing
procedure for knockoffs, leading to a Derandomized Truncated D-vine Copula
Knockoffs with e-values (DTDCKe) procedure. We demonstrate the robustness of
the DTDCKe procedure under various scenarios with extensive simulation studies.
We further illustrate its efficacy using a gene expression dataset, showing it
achieves a more reliable gene selection than other competing methods, when the
findings are compared with those of a meta-analysis. The results indicate that
our Truncated D-vine copula approach is robust and has superior power,
representing an appealing approach for variable selection in different
multivariate applications, particularly in gene expression analysis.
