(山東科技大學(xué) 地球科學(xué)系， 泰安 271019)
摘 要: 合理地選擇參數(shù)， 避免參數(shù)間的強(qiáng)復(fù)共線性， 是參數(shù)有效估計的關(guān)鍵之一。 通過將參數(shù)X分為兩類，即基本參數(shù)X1和附加參數(shù)X2，并假定附加參數(shù)的選取不當(dāng)是造成參數(shù)間強(qiáng)復(fù)共線性的主要原因，提出了用點(X2中的一列向量)到空間(由X1所對應(yīng)的列向量張成Hilbert空間的子空間H0)夾角的正弦值作為度量標(biāo)準(zhǔn)來優(yōu)選附加參數(shù)， 給出了對該方法的理論論證， 并用兩個算例對度量方法進(jìn)行了驗證和說明。
關(guān)鍵字: 參數(shù)估計； 復(fù)共線性； 度量； Hilbert空間
（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
