Choosing trajectory and data type when classifying functional data

In some problems involving functional data, it is desired to undertake prediction or classification before the full trajectory of a function is observed. In such cases, it is often preferable to suffer somewhat greater error in return for making a decision relatively early. The prediction and classification problems can be treated similarly, using mean squared prediction error, or classification error, respectively, as the means for quantifying performance, so in this paper we focus principally on classification. We introduce a method for determining when an early decision can reasonably be made, using only part of the trajectory, and we show how to use the method to choose among data types. Our approach is fully nonparametric, and no specific model is required. Properties of error-rate are studied as functions of time and data type. The effectiveness of the proposed method is illustrated in both theoretical and numerical terms. The classification referred to in this paper would be termed supervised classification in machine learning, to distinguish it from unsupervised classification, or clustering. Copyright 2012, Oxford University Press.