Noisy　and　missing　data　are　often　encountered　in　real　applications　such　that　the　observed　covariates　contain　measurement　errors.　Despite　the　rapid　progress　of　model　selection　with　contaminated　covariates　in　high　dimensions,　methodology　that　enjoys　virtues　in　all　aspects　of　prediction,　variable　selection,　and　computation　remains　largely　unexplored.　In　this　paper,　we　propose　a　new　method　called　as　the　balanced　estimation　for　high-dimensional　error-in-variables　regression　to　achieve　an　ideal　balance　between　prediction　and　variable　selection　under　both　additive　and　multiplicative　measurement　errors.　It　combines　the　strengths　of　the　nearest　positive　semi-definite　projection　and　the　combined　L-1　and　concave　regularization,　and　thus　can　be　efficiently　solved　through　the　coordinate　optimization　algorithm.　We　also　provide　theoretical　guarantees　for　the　proposed　methodology　by　establishing　the　oracle　prediction　and　estimation　error　bounds　equivalent　to　those　for　Lasso　with　the　clean　data　set,　as　well　as　an　explicit　and　asymptotically　vanishing　bound　on　the　false　sign　rate　that　controls　overfitting,　a　serious　problem　under　measurement　errors.　Our　numerical　studies　show　that　the　amelioration　of　variable　selection　will　in　turn　improve　the　prediction　and　estimation　performance　under　measurement　errors.　(C)　2018　Elsevier　B.V.　All　rights　reserved.