Introduction

Abstract

Figure 1.1 provides a prototype for the type of data that we shall consider. It shows the heights of 10 Swiss boys measured at a set of 29 ages in the Zurich Longitudinal Growth Study (Falkner, 1960). The ages are not equally spaced; there are annual measurements from two to 10 years, followed by biannually measured heights. Although great care was taken in the measurement process, there is an uncertainty or noise in height values with a standard deviation of about 5 mm. Even though each record involves only 29 discrete values, these values reflect a smooth variation in height that could be assessed, in principle, as often as desired, and is therefore a height function. Thus, the data consist of a sample of 10 functional observations Height _i (t).