.-第22卷第2期中国科学技术大学学报VOI22,No2rJON^t.oIN^vEsRlosE^EcHNOLoY.eTGFF2年6月皿cH1训竹CI胡湘JU1992n99ConvergeneeRatesofSomeEstimatorsfor许aSemiParametrieRegressionModelGaoJitie()伸rtmntofMatbematiCS)Abst班Ct·`二`,,,-considertheergonmodel犷“心声+夕()+氏for`一l2…,eHer夕15anuneslr,,`.known加netinninIR二(一coco)e15anuno眺erveddlsutrbance刀晚sedonthekernelanneanerrs,eoeonvereesaedesrtihg加estimaot吐,(:)sompt加atsenaret咖t出es往m-a.·torsof刀andg()areobatined二,一,众ywordssemi琳rametrieregre绍fonmodelleastsquareest加ateoPtimalconvegteneerateAMS翻bjeetClas企让.tion(1991):62G07,62J101IntrodutCionConsi血rthemodelgivenby,二梦`一人刀+g(x`)+伙,落一12…,(1),...,,wheer(人:`,e`)are11drandomsamPles(人二`)ande`areindeepndentand氏15hterandomerror,.wihtmean0andvarianceaZ刀15anunkhownParam亡etrand夕15anunknownfunetionoSmeasympto桩etheoryfor钟riteal印lineest加atosrof刀hasboende穴10讲dbyeHekman[i〕and.,`Riee[幻hTeyinvestisat“htecasewheert5aremodeledas,人一h(劣`)+价云=1,2,…,(2)whereh15akno、vnfunetionoftheevoariate劣andthe了`忱havelikeezromaen,uneorrelatedrandom.variables.ReceiVedAPr亚30,1991.辞ThisPro扭tsuPPort目byNNSFCun血rtheconrraet18901001130中国朴学扶术大学学报第22卷,e,eR侧毖ntlysepckman[,]has血vl叩司anatetrnauvesetimaotrof声in(i)hattunderamodl-suhCas(2)wiht夕andhbohtsmooth,is创沼uredof加vinga琳armetrieconver罗ncearetforistsatn·血dterrorandasymtPiotaCllynegl语ibleb边5withouttheneceSiytofundersmohtingia.,hTeasymtP成eanalyseofeHkCman[]anduE恤nketl[月〕aereon份rn司wi小几=0or价一0,,·.`=l2…,wihehaer比战刁on9esitmatedbySPlinesmotbj的9esitmateS:,:`,,InhtePr姗nt劝团ywedlscussthefollowingextremeca,namelythecasewhere=0`=l,,,二.2….andh()=公(iwhtoutl端Ofgenerailyt)Thereforewe创铭umethatthe豹followthernodel(the邢”eificcaseof(1)),,,夕`~脚`+夕(x`)+氏云~12,…,(3).魂,侃enforinetrestinamodelofhtisform咖msform脉workby血bank以以[〕也eother.rnistaesor汕tthissepeifiemodel15themixedergr创沼ionm团elprop汉姆dbyStone[s〕easo,一E匕翻川onhtelea`tqSuaerest血nator几Of刀andthekernelandneaesrtniehgborestimates么of夕·someOPt加alartesofeonvergeneeabout几and纵aer由atined2M.inResultS