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2008 Theoretical properties of Cook’s PFC dimension reduction algorithm for linear regression
Oliver Johnson
Electron. J. Statist. 2: 807-828 (2008). DOI: 10.1214/08-EJS255

Abstract

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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Oliver Johnson. "Theoretical properties of Cook’s PFC dimension reduction algorithm for linear regression." Electron. J. Statist. 2 807 - 828, 2008. https://doi.org/10.1214/08-EJS255

Information

Published: 2008
First available in Project Euclid: 18 September 2008

zbMATH: 1320.62117
MathSciNet: MR2443197
Digital Object Identifier: 10.1214/08-EJS255

Subjects:
Primary: 62H10
Secondary: 62E20

Keywords: principal components , principal fitted components , Random matrix theory , regression

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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