广义岭型主成分估计在降维估计类中的方差最优性质

The Variance Optimality of Combining Generalized Ridge and Principal Components Estimate in the Class of Shrunken Dimension Estinmates

定义了一类降维估计,称为广义岭型降维估计类.在这类降维估计中,用矩阵求特征值的方法研究了广义岭型降维估计的方差最优性质.证明了它的方差阵最小,方差阵的特征值最小.进一步导出了广义岭型主成分估计的方差和、方差阵特征值乘积及方差阵的正交不变范数最小.

The class of reduced-dimension estimate is defined in the paper and it is called a class of generalized ridge reduced-dimension estimate, The variance optimality is studied in the class by the method of obtaining eigenvalue of matrix. It is proved that the combing generalized ridge and principal components estimate has several minimum properties of variance.