Bootstrap confidence intervals for principal response curves

The Principal Response Curve model is of use to analyze multivariate data resulting from experiments involving repeated sampling in time. The time-dependent treatment effects are represented by Principal Response Curves (PRCs), which are functional in nature. The sample PRCs can be estimated using a raw approach, or the newly proposed smooth approach. The generalizability of the sample PRCs can be judged using confidence bands. The quality of various bootstrap strategies to estimate such confidence bands for PRCs is evaluated. The best coverage was obtained with BCa intervals using a nonparametric bootstrap. The coverage appeared to be generally good, except for the case of exactly zero population PRCs for all conditions. Then, the behaviour is irregular, which is caused by the sign indeterminacy of the PRCs. The insights obtained into the optimal bootstrap strategy are useful to apply in the PRC model, and more generally for estimating confidence intervals in singular value decomposition based methods.