Analysis of discretely sampled functional data based on robust estimation of dispersion.

Estimating dispersion is a central problem in functional/longitudinal data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one can encounter in the functional setting. To remedy these deficiencies we introduce a family of resistant dispersion estimators from discretely sampled functional data. The proposed method combines M-estimation and regularization with the powerful thin-plate penalty and is suitable for both commonly and independently observed trajectories that are subject to measurement error. The goals of this project are the theoretical investigation of this family of estimators, including conditions for their existence and asymptotic rates of convergence, the development of a fast computational procedure and the exploration of numerous possible applications in the fields of functional data analysis and non-parametric regression.