Theoretical properties of Cook's PFC dimension reduction algorithm for linear regression
Abstract
Description
We analyse the properties of the Principal Fitted Components (PFC) algorithm proposed by Cook. We derive theoretical properties of the resulting estimators, including sufficient conditions under which they are $\sqrt{n}$-consistent, and explain some of the simulation results given in Cook's paper. We use techniques from random matrix theory and perturbation theory. We argue that, under Cook's model at least, the PFC algorithm should outperform the Principal Components algorithm.
Published in at http://dx.doi.org/10.1214/08-EJS255 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Published in at http://dx.doi.org/10.1214/08-EJS255 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)