  Outlying curves often occur in functional or longitudinal datasets, and can
be very influential on parameter estimators and very hard to detect visually.
In this article we introduce estimators of the mean and the principal
components that are resistant to, and then can be used for detection of,
outlying sample trajectories. The estimators are based on reduced-rank t-models
and are specifically aimed at sparse and irregularly sampled functional data.
The outlier-resistance properties of the estimators and their relative
efficiency for noncontaminated data are studied theoretically and by
simulation. Applications to the analysis of Internet traffic data and glycated
hemoglobin levels in diabetic children are presented.
