Shape-Invariant Models for Non-Independent Functional Data

Abstract

Non-independent functional data frequently arise in evolutionary and biological studies. It is important to possess models that incorporate correlations between subjects and appropriately describe the relationships between response and covariates. The variation in the response curves is usually a mixture of amplitude and phase variation, both of which should be explicitly modeled for efficient statistical inference. In this dissertation we propose a shape-invariant model that explicitly addresses amplitude and phase variability. We incorporate genetic and environmental random effects for the parameters, and use the additive genetic information matrix in the representation of the covariance matrices to make the unobservable genetic components mathematically identifiable. We derive the asymptotic properties of the maximum likelihood estimators and study their finite sample behavior by simulation. Then we apply the new method to the analysis of growth curves of flour beetles.