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基于高阶差分方法半参数回归模型参数估计及其minimax性质.docx

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基于高阶差分方法半参数回归模型参数估计及其minimax性质 Abstract: High-orderdifferenceapproximationmethodsarecommonlyusedinsemiparametricregressionmodelsforparameterestimation.Thispaperinvestigatestheuseofhigh-orderdifferencemethodsinsemiparametricregressionmodelsandtheirminimaxproperties.Inthispaper,wediscusssomeofthepropertiesofhigh-orderdifferencemethodsandexplorehowtheycanbeusedtoestimatetheparametersofsemiparametricregressionmodels.Theresultsofthisstudyshowthathigh-orderdifferencemethodscanbeusedtoaccuratelyestimatetheparametersofsemiparametricregressionmodels. Introduction: Semiparametricregressionmodelsareusedtodescribetherelationshipbetweenasetofexplanatoryvariablesandaresponsevariableundertheassumptionthattherelationshipisnotfullyknown.Thesemodelsareusefulinavarietyoffieldssuchaseconomics,statistics,andengineering. Oneapproachtoestimatingtheparametersofsemiparametricregressionmodelsisthroughtheuseofhigh-orderdifferencemethods.Thesemethodsutilizethedifferencebetweenthefunctionvaluesatadjacentpointstoapproximatethederivativesoftheregressionfunction. Inthispaper,weexploretheuseofhigh-orderdifferencemethodsinsemiparametricregressionmodelsandtheirminimaxproperties.Wewilldiscusssomeofthepropertiesofhigh-orderdifferencemethodsandexaminehowtheycanbeusedtoestimatetheparametersofsemiparametricregressionmodels. Background: Semiparametricregressionmodelsareaclassofmodelsthatcombineparametricandnon-parametriccomponents.Theparametriccomponentismodeledusingalinearorgeneralizedlinearmodel,whilethenon-parametriccomponentismodeledusingfunctionsthatdonotdependonanyspecificdistributionalassumption.Non-parametriccomponentsareoftenusedwhenthereisalimitedamountofdataand/orwhenthedatafollowanon-standarddistribution.Examplesofnon-parametricregressionfunctionsincludesplines,kernelsmoothing,andlocalpolynomialregression. High-orderdifferencemethodsareaclassofnumericalmethodsthatusethedifferencebetweenfunctionvaluesatadjacentpointstoapproximatethederivativesofafunction.Thesemethodsarecommonlyusedinnumericalana