Multiple Loci Mapping via Model‐free Variable Selection

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