OPTIMALITY OF PRINCIPAL COMPONENTS AND A NEW CLASS OF PRINCIPAL COMPONENTS ESTIMATES

The paper deals with the variation and regression optimality of principal components (PO). It is shown that the PC estimate of regression coefficients has several types of minimum-variance properties. For the variation optimality, the covarianee matrix of PC of a random veeton is maximal in the senoe of matrix partial ordering. A new class of PC estimates of regression coefficients is introduced and its superiority over ordinary least squares estimate is demonstrated. The fact that most of biased estimates are the members of this class gives a new insight into the nature of these estimates. A simpler computation formula of ridge trace, which is simpler than the one given by Hoerl-Kennard, is also given.