Department of Statistics, UCLA

Brumback and Rice are to be congratulated for this neat and excellent paper on the smoothing spline models for the analysis of nested and crossed samples of curves. Of particularly important are the connections between smoothing spline methods and the mixed e ects models. Such connections are not only important in our intuitive understanding of the smoothing spline methods, but also elegant in deriving methods for selecting smoothing parameters. With modern technology, data can nowadays easily be collected in a form of curves. Fully processing the information contained in the sample curves is a challenging and emerging subject in statistics. The subject has strong connections with traditional longitudinal data analysis (see for example Diggle, Liang and Zeger 1994 and Hand and Crowder 1996). The ideas presented in the Brumback and Rice and this discussion are expected to have strong impact on both functional data analysis and longitudinal data analysis. We welcome the opportunity to make a few comments and to present other simple alternative methods that will be helpful for the future development of the subject.