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We propose a distance between two realizations of a random process where foreach realization only sparse and irregularly spaced measurements withadditional measurement errors are available. Such data occur commonly inlongitudinal studies and online trading data. A distance measure then makes itpossible to apply distance-based analysis such as classification, clusteringand multidimensional scaling for irregularly sampled longitudinal data. Once asuitable distance measure for sparsely sampled longitudinal trajectories hasbeen found, we apply distance-based clustering methods to eBay online auctiondata. We identify six distinct clusters of bidding patterns. Each of thesebidding patterns is found to be associated with a specific chance to obtain theauctioned item at a reasonable price.

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