Index Models for Sparsely Sampled Functional Data

However, a common complication in functional data analysis is one of sparsely observed curves, that is predictors that are observed, with error, on a small subset of the possible time points. Such sparsely observed data induce an errors-in-variables model, where one must account for measurement error in the functional predictors.

Faced with sparsely observed data, most current functional regression methods simply estimate the unobserved predictors and treat them as fully observed; thus failing to account for the extra uncertainty from the measurement error. We propose a new functional errors-in-variables approach, sparse index model functional estimation (SIMFE), which uses a functional index model formulation to deal with sparsely observed predictors.