The Florida State University College of Arts and Sciences Bootstrap Prediction Bands for Non-parametric Random Function Signals

Methods employed in the construction of prediction bands for continuous curves require a different approach to those used for a data point. In many cases, the underlying function is unknown and thus a distribution-free approach which preserves sufficient coverage for the entire signal is necessary in the signal analysis. This paper discusses three methods for the formation of (1-α)100% bootstrap prediction bands and their performances are compared through the coverage probabilities obtained for each technique. Bootstrap samples are first obtained for the signal and then three different criteria are provided for the removal of α100% of the curves resulting in the (1-α)100% prediction band. The first method uses the area between the upper and lower curves as a gauge to extract the widest bands in the dataset of signals. Also investigated are extractions using the Hausdorff distance between the bounds as well as an adaption to the bootstrap intervals discussed in Lenhoff et al (1999).[15] The bootstrap prediction bands each have good coverage probabilities for the continuous signals in the dataset. For a 95% prediction band, the coverage obtained were 90.59%, 93.72% and 95% for the L Distance, Hausdorff Distance and the adjusted Bootstrap methods respectively. The methods discussed in this paper have been applied to constructing prediction bands for spring discharge in a successful manner giving good coverage in each case. Spring Discharge measured over time can be considered as a continuous signal and the ability