部分线性分位数回归模型的平均估计胡国治，曾婕（合肥师范学院数学与统计学院，安徽合肥230601）摘要：模型平均估计可对不同候选模型中的参数估计量进行加权平均，能有效提高参数估计的精度，在经济、金融和管理等领域有着广泛应用。为提高部分线性分位数回归模型的参数估计效果，本文构造了基于兴趣参数的模型平均估计量并探究了其大样本性质。首先，利用B样条近似非参数函数，并通过极小化分位数损失函数来得出各候选模型的回归系数估计量，在局部误设定框架下推导了系数估计量的渐近分布；其次，基于候选模型中兴趣参数的估计构造出了模型平均估计量，并得出其渐近性质；最后，推导了覆盖真实参数的概率趋近于名义水平的置信区间。本文研究不仅丰富了平均估计的渐近分布理论，而且为兴趣参数构造了合适的置信区间。关键词：部分线性模型；分位数回归；模型选择；模型平均中图分类号：O212.7文献标志码：A文章编号：1007-4260（2023）01-0032-05AveragingEstimationforPartiallyLinearQuantileRegressionModelsHUGuozhi,ZENGJie(CollegeofMathematicsandStatistics,HefeiNormalUniversity,Hefei230601,China)Abstract:Modelaveragingestimatorisaweightedaverageoftheparameterestimatorsindifferentcandidatemodels,whichcaneffectivelyimprovetheaccuracyofparameterestimationandhaswideapplicationsinthefieldsofeconomy,fi-nanceandmanagement.Inordertoimprovetheparameterestimationeffectforpartiallylinearquantileregressionmodel,thispaperconstructsthemodelaveragingestimatorofthefocusparameterandexploresitslargesamplenature.Firstly,thenon-parametricfunctionisapproximatedbyB-spline,andtheregressioncoefficientestimatorineachcandidatemodelisobtainedbyminimizingthequantilelossfunction.Underthemisspecificationframework,theasymptoticdistributionoftheregressioncoefficientestimatorineachsubmodelisobtained.Secondly,basedontheestimatorsofthefocusparameterinthecandidatemodel,themodelaveragingestimatorisconstructed,anditsasymptoticpropertyisobtained.Finally,aconfidenceintervalwithanactualcoverageprobabilitythatconvergestotheintendedlevelisconstructed.Thispapernotonlyobtainstheasymp-toticdistributiontheoryofthemodelaveragingestimator,butalsoconstructsanappropriateconfidenceint...
