Abstract:
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Sparsely-structured functional data are curves whose interesting features, such as spikes, make up a small proportion of each curve. To model such curves in a range of complex designs, such as nested structures, a flexible modeling procedure which models within and between subject variation while performing model selection to exclude predictors corresponding to the irrelevant parts of the curves is needed. We propose a semiparametric nonlinear mixed effects model for the analysis of sparsely-structured functional data. The mean curves are modeled nonparametrically using data-driven basis expansion and subject-specific deviations in the mean curves are modeled using parametrically specified random effects. Penalized likelihood with the Adaptive Lasso provides a unified criterion for joint model selection and estimation. A back-fitting algorithm using the Laplace Approximation is proposed for estimation and sampling properties of resulting estimates, whose variation account for the joint estimation of the shape functions, fixed and random effects, and variance components, are proved. We assess our procedure through simulation and its application to a chromatographic dataset.
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