Theoretical properties of Cook's PFC dimension reduction algorithm for linear regression

Details Theoretical properties of Cook's PFC dimension reduction algorithm for linear regression Theoretical properties of Cook's PFC dimension reduction algorithm for linear regression

2008-06-25

arxiv.org/abs/0806.4120v2

Electronic Journal of Statistics 2008, Vol. 2, 807-828

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS255 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS255

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.

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