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

by Oliver Johnson

The analysis of many statistical problems is complicated by the fact that data often lies in a high-dimensional space. This increases the uncertainty associated with many algorithms, and is often referred to as `the curse of dimensionality'. Many authors use the method of Principal Components to find a simpler version of the problem, while capturing the essential variation that exists. Recently, Dennis Cook has proposed the related Principal Fitted Components (PFC) algorithm, which works in a similar way, but takes more advantage of the data. Oliver Johnson has published a paper analysing the performance of Cook's algorithm, and explaining some of the simulation results he gives. Johnson gives conditions under which PFC will perform well, and shows that in certain situations it will outperform the more standard Principal Components algorithm.

Keywords: Principal Components, Principal Fitted Components, random matrix theory, regression.

Full text of the paper, which has recently appeared in Electronic Journal of Statistics.