岭型主成分估计的方差最优性质

Variance Optimalities of Combining Ridge and Principal Components Estimate

研究岭型主成分估计在降维估计类中的方差最优性,证明了它的方差阵在降维估计类中最小,方差阵的特征值最小,方差和及方差积最小。并讨论了它的方差在正交不变范数意义下的最小性和方差的最小最大性质,得出了方差阵的行列式及正交范数在降维估计类中最小。

The variance optimality of combining ridge and principal components estimate is discussed in the class of reduced-dimension estimates. And it is proved that it has minimum variance of sum and multiplication of variance. The minimax property of variance in the sense of orthogonal unchanged norm is studied.