简介:Itiswellknownthatwhentherandomerrorsareiid.withfinitevariance,theweekandthestrongconsistencyofLSestimateofmultipleregressioncoefficientsareequivalent.Thisnote,byconstructingacounter-example,showsthatthisequivalencenolongerholdstrueincasethattherandomerrorspossessonlyther-thmomentwith1≤r<2.
简介:基于平衡损失的思想和最小二乘统一理论,对带线性约束的一般线性模型提出了一种全面度量估计优良性的标准.给出了此标准下模型中回归系数线性函数的约束广义平衡LS估计,并得到了约束广义平衡LS估计唯一性的一个充分条件.
简介:Inthiswork,somechemometricsmethodsareappliedforthemodelingandpredictionoftheHildebrandsolubilityparameterofsomepolymers.Ageneticalgorithm(GA)methodisdesignedfortheselectionofvariablestoconstructtwomodelsusingthemultiplelinearregression(MLR)andleastsquare-supportvectormachine(LS-SVM)methodsinordertopredicttheHildebrandsolubilityparameter.TheMLRmethodisusedtobuildalinearrelationshipbetweenthemoleculardescriptorsandtheHildebrandsolubilityparameterforthesecompounds.ThentheLS-SVMmethodisutilizedtoconstructthenon-linearquantitativestructure-activityrelationship(QSAR)models.TheresultsobtainedusingtheLS-SVMmethodarethencomparedwiththoseobtainedfortheMLRmethod;itwasrevealedthattheLS-SVMmodelwasmuchbetterthantheMLRone.Theroot-mean-squareerrorsofthetrainingsetandthetestsetfortheLS-SVMmodelwere0.2912and0.2427,andthecorrelationcoefficientswere0.9662and0.9518,respectively.ThispaperprovidesanewandeffectivemethodforpredictingtheHildebrandsolubilityparameterforsomepolymers,andalsorevealsthattheLS-SVMmethodcanbeusedasapowerfulchemometricstoolforthequantitativestructure-propertyrelationship(QSPR)studies.