M-estimation　is　a　widely　used　technique　for　robust　statistical　inference.　In　this　paper,　we　investigate　the　asymptotic　properties　of　a　nonconcave　penalized　M-estimator　in　sparse,　high-dimensional,　linear　regression　models.　Compared　with　classic　M-estimation,　the　nonconcave　penalized　M-estimation　method　can　perform　parameter　estimation　and　variable　selection　simultaneously.　The　proposed　method　is　resistant　to　heavy-tailed　errors　or　outliers　in　the　response.　We　show　that,　under　certain　appropriate　conditions,　the　nonconcave　penalized　M-estimator　has　the　so-called　＂Oracle　Property＂;　it　is　able　to　select　variables　consistently,　and　the　estimators　of　nonzero　coefficients　have　the　same　asymptotic　distribution　as　they　would　if　the　zero　coefficients　were　known　in　advance.　We　obtain　consistency　and　asymptotic　normality　of　the　estimators　when　the　dimension　p(n)　of　the　predictors　satisfies　the　conditions　p(n)　log　n/n　-＞　0　and　p(n)(2)/n　-＞　0,　respectively,　where　n　is　the　sample　size.　Based　on　the　idea　of　sure　independence　screening　(SIS)　and　rank　correlation,　a　robust　rank　SIS　(RSIS)　is　introduced　to　deal　with　ultra-high　dimensional　data.　Simulation　studies　were　carried　out　to　assess　the　performance　of　the　proposed　method　for　finite-sample　cases,　and　a　dataset　was　analyzed　for　illustration.