Abstract: Functional data analysis has received considerable recent attention and a number of successful applications have been reported. In this paper, asymptotically simultaneous confidence bands are obtained for the mean function of the functional regression model, using piecewise constant spline estimation. Simulation experiments corroborate the asymptotic theory. The confidence band procedure is illustrated by analyzing CD4 cell counts of HIV infected patients.
Key words and phrases: B spline, confidence band, functional data, Karhunen-Loève L² representation, knots, longitudinal data, strong approximation.