Keeping greed good: sparse regression under design uncertainty with   application to biomass characterization
  In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated measurements on both the design and dependent variables may be leveraged to enhance a sparse regression algorithm. Specifically, we estimate the variance and use it to scale our design variables. We demonstrate the efficacy of scaling from several points of view and validate it empirically with a biomass characterization data set using two of the most widely used sparse algorithms: least angle regression (LARS) and the Dantzig selector (DS). 
David J. Biagioni and Ryan Elmore and Wesley Jones
stat.AP stat.CO stat.ME stat.ML