(山东科技大学 地球科学系， 泰安 271019)
摘 要: 合理地选择参数， 避免参数间的强复共线性， 是参数有效估计的关键之一。 通过将参数X分为两类，即基本参数X1和附加参数X2，并假定附加参数的选取不当是造成参数间强复共线性的主要原因，提出了用点(X2中的一列向量)到空间(由X1所对应的列向量张成Hilbert空间的子空间H0)夹角的正弦值作为度量标准来优选附加参数， 给出了对该方法的理论论证， 并用两个算例对度量方法进行了验证和说明。
关键字: 参数估计； 复共线性； 度量； Hilbert空间
（Department of Geoscience, Shandong University of Science and Technology, Tai′an 271019, P.R.China）
Abstract:Properly selecting parameters to avoid stronger multicollinearity is a key to efficient estimation of parameters. Through separating parameters X into basic parameter X1 and additional parameter X2, and assuming that nonproperly choosing additional parameters is the main reason causing stronger multicollinearity among parameters, the measure criterion which applies sine of the angle from a point (a vector in X2) in Hilbert space to space H 0 (a subspace of Hilbert space, from columns of X1) was proposed to optimumize the additional parameters. Theoretical reasoning and two demonstration spanded examples were also given.
Key words: parameter estimation; multicollinearity; measures; Hilbert space
