On a Statistical Model for Principal Component Analysis

Martin Schlather (University of Mannheim)

Wednesday 3rd July 13:00-14:00 Maths 110

Abstract

The difference between a numerical recipe and statistical inference is the existence of a statistical model. Since dimension reduction leads to lower dimensional distributions, the latter have to be clearly included in the statistical model. Hence, from my point of view, PCA as well as submodel selection in linear regression have been numerical recipes only. On the other hand,
a canonical approach to PCA for extreme values, where the existence of the theoretical covariance is not guaranteed, has been vainly searched for decades. In my talk, I give a general approach to a statistical model for dimension reduction, which includes all three above mentioned situations as
special cases.

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