Visualizing Functional Data with an Application to eBay’s Online Auctions

Abstract

Technological advances in the measurement, collection, and storage of data have led tomore andmore complex data structures. Examples of such structures include measurements of the behavior of individuals over time, digitized two- or three-dimensional images of the brain, and recordings of three- or even four-dimensional movements of objects traveling through space and time. Such data, although recorded in a discrete fashion, are usually thought of as continuous objects that are represented by functional relationships. This gave rise to functional data analysis (FDA), which was made popular by the monographs of Ramsay and Silverman (1997, 2002), where the center of interest is a set of curves, shapes, objects, or, more generally, a set of functional observations, in contrast to classical statistics where interest centers on a set of data vectors. In that sense, functional data is not only different from the data structure studied in classical statistics, but it actually generalizes it. Many of these new data structures require new statistical methods to unveil the information that they carry.