Asymptotic and bootstrap confidence bounds for the structural average of curves

For analyzing samples of curves, Kneip and Gasser proposed a “structural analysis” for estimating an average curve which gives the average amplitude and dynamics of the sample curves. An important step of their method is the estimation of the warping functions in order to eliminate the differences in dynamics between different curves. It is of interest to compute confidence bounds for the structural average curve. First, we derive the necessary asymptotic results to obtain confidence intervals based on asymptotic normality. Due to the complex form of the asymptotic formulas and due to their asymptotic nature, bootstrap procedures are studied in a second step. A small archive SACI (Structural Averaging and Confidence Intervals), written in Fortran, can be obtained from the Web site “http://www.unizh.ch/biostat” to compute the structural average curve, to construct confidence regions at a structural point and to compute confidence bars at other points.