Conference Agenda

We revisit the classic situation in functional data analysis in which data items such as curves are observed at discrete (possibly sparse and irregular) arguments with observation noise. We focus on the reconstruction of individual curves, especially on prediction intervals and prediction bands for them. The standard approach is to proceed in two steps: First, one estimates the mean and covariance function of curves and observation noise variance function by smoothing techniques such as penalized splines. Second, under Gaussian assumptions, one derives the conditional distribution of a curve given its noisy discrete observations and constructs prediction sets with required properties (usually employing sampling from the predictive distribution). This approach is indeed well established, commonly used and theoretically valid but practically, it surprisingly fails in its key property: prediction sets constructed this way often do not have the required coverage. The actual coverage is lower than the nominal one. This has been little reported and studied in the literature. We investigate the cause of this issue and propose a remedy.