The linear Lasso: A location model approach

Abstract

AbstractWe use location model methodology to guide the least squares analysis in the Lasso problem of variable selection and inference. The nuisance parameter is taken to be an indicator for the selection of explanatory variables, and the interest parameter is the response variable itself. Recent theory eliminates the nuisance parameter by marginalization on the data space and then uses the resulting distribution for inference concerning the interest parameter. We develop this approach and find that primary inference is essentially one‐dimensional rather than n‐dimensional, inference focuses on the response variable itself rather than the least squares estimate (as variables are removed), computation is relatively easy, a scalar marginal model is available, and ineffective variables can be removed by distributional tilt or shift.