Large numbers of explanatory variables: a probabilistic assessment.

Recently, Cox and Battey (2017 Proc. Natl Acad. Sci. USA 114, 8592-8595 (doi: 10.1073/pnas.1703764114)) outlined a procedure for regression analysis when there are a small number of study individuals and a large number of potential explanatory variables, but relatively few of the latter have a real effect. The present paper reports more formal statistical properties. The results are intended primarily to guide the choice of key tuning parameters.