Regression analysis is a powerful tool for the study of changes in a dependant variable as a function of an independent regressor variable.
When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques~\cite{wand95,hardle90} are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using {\em flat Euclidean spaces} undermines our ability to represent natural biological variability. In this talk I will develop a method for regression analysis of general, manifold-valued data. Specifically, we extend Nadaraya-Watson kernel regression by recasting the regression problem in terms of Fr\'echet expectation. Although this method is quite general, our driving problem is the study anatomical shape-change as a function of age from random-design image data.
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