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 -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.
|Translated title of the contribution||Theoretical properties of Cook’s PFC dimension reduction algorithm for linear regression|
|Pages (from-to)||807 - 828|
|Number of pages||22|
|Journal||Electronic Journal of Statistics|
|Publication status||Published - 2008|