Principal Components And Long Run Implications Of Multivariate Diffusions

The authors investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but they allow for a general class of constraints and multivariate densities, including densities without compact support and even densities with algebraic tails. They provide primitive sufficient conditions for the existence of these principal components. They characterize the limiting behavior of the associated eigenvalues, the objects used to quantify the incremental importance of the principal components.