Chapter 30: Functional Data Analysis

James O. Ramsay

Functional data analysis Functional data analysis explores samples of data where each observation arises from a curve or function. We require the data to provide enough information to estimate the curve and its properties that we wish to use. For example, Figure 30.1 displays one of 50 replications of the writing of ‘statistical science’ in Chinese described in Ramsay (2000). The curve is multivariate, being a trajectory in three-dimensional space: two coordinates X and Y on the writing surface plus the vertical coordinate Z . The location of the tip of the pen was recorded 400 times per second over the roughly six seconds required to write the script, with an error level of about 0.5 millimeters. This may sound like a lot of data, but there are 50 pen strokes, some of which have consistently sharp structures, and we have even more highly localized events, such as effects of ...

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