Variable Selection in Seemingly Unrelated Regressions with Random   Predictors
  This paper considers linear model selection when the response is vector-valued and the predictors are randomly observed. We propose a new approach that decouples statistical inference from the selection step in a "post-inference model summarization" strategy. We study the impact of predictor uncertainty on the model selection procedure. The method is demonstrated through an application to asset pricing. 
David Puelz, P. Richard Hahn, Carlos Carvalho
stat.ME