1、合肥工業(yè)大學(xué)碩士學(xué)位論文基于相依函數(shù)型數(shù)據(jù)的穩(wěn)健估計(jì)研究姓名：程偉申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：凌能祥20100401AStudyonRobustEstimateforDependentFunctionalDataAbstractOverthepastdecades，thefunctionaldata，arisingfromCro州hcurveanalysis，TaxonomyBiomechanics，Medicineand

2、etc，hasbeendevelopingontoahighlynewlevelHoweverduetoitsabundanceinrelateddisciplines，thetheoryoffunctionaldatastillneedstobeexploredfurthertosolvethenewproblemsThisdissertationaimsatsolvingtwoproblemsasfollowsFirstlywein

3、vestigatethenonparametrickernelestimatorsforaregressionfunctionwhenresponsevariabletakevaluesinRandexplanatoryvariableisvaluedinsomeabstractfunctionspaceFBytherobustmethod，weestablishthealmostcompleteconvergencerateofthe

4、estimatorsfordependentfunctionaldatawhichextendtheexistingliteraturerelatedresultsiniidcaseSecondly，weinvestigateakernelestimationofconditionalquantilewithrobustproperty，andavoidsomeproblemsoccurringinthedouble—kernelmet

5、hodwhenresponsevariabletakevaluesinRandexplanatoryvariableisvaluedinsomeabstractspaceFwiththeassociatedsemimetricdenotedbyd(，)，whichiscalledfunctionrandomvariablesWhentheobservationsaredependent，weestablishthealmostcompl

6、eteconvergencerateoftheestimatorsundersomeconditionsAllwehavedoneinthisdissertationextendtheexistingliteraturerelatedresultsKeywords：dependentfunctionaldata；robustkernelestimator；conditionalquantileestimate；almostcomplet