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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.
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