Abstract
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.
Highlights
We consider studies of dependence in which there are relatively few individuals on each of which a large number of potential explanatory variables are measured
The present paper reports more formal statistical properties
Suppose that v variables are to be assessed for their explanatory power for a response variable
Summary
We consider studies of dependence in which there are relatively few individuals on each of which a large number of potential explanatory variables are measured. Powerful procedures for analysis emanate from the lasso [1] (for a discussion of the mathematical aspects, see [2]) They aim to uncover a single small set of signal variables effective for prediction. Those small sets of potential signal variables that give essentially the same fit; choice between different sets requires either more data or specific subject–matter information. Their procedure allowed informal checks standard in much statistical work, such as those for nonlinearity, interaction or anomalous individuals. The ideas involved apply rather generally, for example, to likelihood-based fitting of logistic models for binary data
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