Detecting and handling outlying trajectories in irregularly sampled functional datasets

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.