Distance-based clustering of sparsely observed stochastic processes, with applications to online auctions

Abstract

We propose a distance between two realizations of a random process where for each realization only sparse and irregularly spaced measurements with additional measurement errors are available. Such data occur commonly in longitudinal studies and online trading data. A distance measure then makes it possible to apply distance-based analysis such as classification, clustering and multidimensional scaling for irregularly sampled longitudinal data. Once a suitable distance measure for sparsely sampled longitudinal trajectories has been found, we apply distance-based clustering methods to eBay online auction data. We identify six distinct clusters of bidding patterns. Each of these bidding patterns is found to be associated with a specific chance to obtain the auctioned item at a reasonable price.

Published in at http://dx.doi.org/10.1214/08-AOAS172 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Describing disability through individual-level mixture models for multivariate binary data
• Functional Data Analysis in Electronic Commerce Research
• The BARISTA: A model for bid arrivals in online auctions

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