Abstract
Functionaldataiswidelyappliedinourdailylife,suchashumanheightgrowth,circadianrhythmsandinternettracanalysisetc.Outliersoftenoccurinfunctionaldata,andsome-timesarediculttodirectlydetectbyvisualinspectionandcauseincorrectconclusioninthestatisticalanalysis.Thus,themethodswhichcanhandleoutliersautomaticallyandecientlyisanimportantissue.Inthispaper,weproposeamethodtohandleandagainstoutliersonparameterestimation.TheestimatorsarebasedonStudent'stdistribution,andwhichcanautomaticallydetectoutliers.Inaddition,theoutlierwillberesistedviaaweightfunction,andthusenhancerobustness.Intheoreticallyderivation,weintroducetheconsistencypropertyofestimatorsandanalyzetheoutliersensitivityandtheasymp-toticcovariancebyderivingtheirinuencefunction.Ournumericalresultsdemonstrateourproposedestimatorsarerobustandcanecientlyagainstoutliers.