功能資料(Functional Data)廣泛應用在我們的日常生活，例如人類的身高增長曲線、醫學上的生理週期和網路流量的分析等等…。離群值(Outliers)經常發生在功能資料中，而且有時候很難直接透過肉眼目測直接的檢測出來。離群值的存在會在統計分析中會導致不正確的結果，例如：數據模型建構上的錯誤、偏差的估測結果等等…。因此，一個能夠自動的並且有效率的來處理離群資料的方法是一個重要的課題。在本文中，我們提出一個在功能資料分析中，進行參數估測程序時可以處理並且抵抗離群值的方法。該估測器是基於觀察值為t分佈的假設，並且由理論推導結果顯示能夠自動地來檢測出離群值。此外，經由一個加權函數，離群值能夠被向下加權以減少對參數估測的影響，從而提高強健性。在理論分析部分，我們討論估測器的一致性(Consistency)分析，並經由推導其影響函數(Influence Function)來分析估測器對於離群值的靈敏性(Sensitivity)。而在數值分析結果中顯示我們所提出的估測器是強健的，並且能夠有效的對抗離群值。

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

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