Discussion of ''Functional Modelling''

Abstract

There is an obvious trend in the current development of new statistical methodology towards attacking considerably more complex data analytic problems. Sometimes development opens up completely new perspectives, while basic ideas may still have their roots in the established theory. The field of functional data analysis seems to hold great promise of this kind. In his review paper, Muller emphasizes the analogy with the development of multivariate data analysis, as a major step forward in statistical thinking which occurred a relatively long time ago. Such methods nowadays form part of the standard repertoire of statistical procedures used in many areas, although the practical interpretation of results is not always straightforward. Considering Muiller's ideas, similar more serious problems may be encountered in the transition to the infinite dimensional procedures of functional data analysis. It is worth noticing that the old problem of obtaining a meaningful practical interpretation of principal components in applied multivariate analysis reappears in a slightly different form in the functional principal components analysis. It will be of great interest to observe whether the same areas of application that have embraced ordinary multivariate statistics will also take advantage of the new infinite dimensional approach. Development in this area should not be judged solely on the basis of what can be achieved by practitioners with the methods offered initially. Thus it is important to stimulate further work dealing with the necessary theoretical framework. The simple observation that new statistical methods are made available, for example, in the analysis of random trajectories, should testify to the willingness of the statistical profession to take up challenges presented by complex practical problems. At this stage, it is difficult to say which methods will stand the test of time. Fundamental ideas developed may turn out to be more important than particular techniques.