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

OT Johnson

doi:10.1214/08-EJS255

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

OT Johnson

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

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 -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
Original language	English
Pages (from-to)	807 - 828
Number of pages	22
Journal	Electronic Journal of Statistics
Volume	2
DOIs	https://doi.org/10.1214/08-EJS255
Publication status	Published - 2008

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title = "Theoretical properties of Cook{\textquoteright}s PFC dimension reduction algorithm for linear regression",

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 -consistent, and explain some of the simulation results given in Cook{\textquoteright}s paper. We use techniques from random matrix theory and perturbation theory. We argue that, under Cook{\textquoteright}s model at least, the PFC algorithm should outperform the Principal Components algorithm.",

author = "OT Johnson",

year = "2008",

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language = "English",

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journal = "Electronic Journal of Statistics",

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N2 - 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.

AB - 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.

U2 - 10.1214/08-EJS255

DO - 10.1214/08-EJS255

M3 - Article (Academic Journal)

SN - 1935-7524

VL - 2

SP - 807

EP - 828

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

ER -

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

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