Economical Models for Functional Covariation - SAMSI

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Overview Functional PCA finite element basis Estimation Examples Extensions and discussion Structured variance–covariance matrices are familiar in multivariate data analysis: band-structured block diagonal patterned parametric models Structure is important when the number of variables p gets at all large because one often needs to use fewer than p(p + 1)/2 degrees of freedom to represent covariance, esp. in mixed effect designs. It may also be that variables are clustered or organized in other ways. Confirmatory factor analysis and structural equation modeling are the usual methods for structured covariance problems. The need for nonparametric functional models of covariance
Overview Functional PCA finite element basis Estimation Examples Extensions and discussion Longitudinal data analysis for equi-spaced times When the number of time points n becomes at all large (5 or more), it can be critical to conserve degrees of freedom used to represent covariation, and especially for mixed effect designs It can be reasonable to assume that covariances are substantial over only limited time lags Stationary and band-structured covariance structures are often used.
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Economical Models for Functional Covariation - SAMSI

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