Title: Model diagnostics for discretely sampled functional data
Authors: Siegfried Hoermann - Graz University of Technology (Austria) [presenting]
Fatima Jammoul - Graz University of Technology (Austria)
Abstract: In practice, functional data are recorded on a discrete set of observation points. A common assumption in the literature is that these discrete measurements are blurred with white noise. Hence, in order to estimate the latent curves, some preprocessing is needed. Common techniques are kernel smoothing, non-linear regression, spline fitting, etc. Although such methods are massively applied in real data implementations, we seldom see those empirical analyses accompanied by diagnostic checks, evaluating the quality or suitability of the chosen preprocessing method. We consider functional data which are recorded on a regular time grid. Hence, the residuals related to each such functional datum may be viewed as a time series. If the preprocessing is accurately executed, these residuals should roughly behave like a white noise sequence. We illustrate, on the basis of some toy data, that for standard preprocessing techniques, this is often not the case. Rather we observe spurious periodicity in the residuals' autocovariance function. We will discuss this phenomenon and establish a suitable inferential framework for testing the white noise hypothesis.