• Adaptive Lasso;
  • Epistatic interaction;
  • Grouped Lasso;
  • Iterative adaptive Lasso;
  • Model-free variable selection;
  • Multiple loci mapping;
  • Multivariate group-wise adaptive penalization;
  • Sliced inverse regression

Summary Despite recent flourish of proposals on variable selection, genome-wide multiple loci mapping remains to be challenging. The majority of existing variable selection methods impose a model, and often the homoscedastic linear model, prior to selection. However, the true association between the phenotypical trait and the genetic markers is rarely known a priori, and the presence of epistatic interactions makes the association more complex than a linear relation. Model-free variable selection offers a useful alternative in this context, but the fact that the number of markers p often far exceeds the number of experimental units n renders all the existing model-free solutions that require n > p inapplicable. In this article, we examine a number of model-free variable selection methods for small-n-large-p regressions in the context of genome-wide multiple loci mapping. We propose and advocate a multivariate group-wise adaptive penalization solution, which requires no model prespecification and thus works for complex trait-marker association, and handles one variable at a time so that works for n < p. Effectiveness of the new method is demonstrated through both intensive simulations and a comprehensive real data analysis across 6100 gene expression traits.