The wide and growing popularity of online auctions creates enormous amounts of publicly available bid data providing an important topic for research. These data pose unique statistical challenges because of their special structures. This research focuses on methods for representing, visualizing, and modeling such data.

We find semi-continuous data manifested in auction consumer surplus data. Semi-continuous data arise in many applications where naturally continuous data become contaminated by the data generating mechanism. The resulting data contain several values that are too-frequent", a hybrid between discrete and continuous data. The main problem is that standard statistical methods, which are geared towards continuous or discrete data, cannot be applied adequately to semi-continuous data. We propose a new set of two transformations for semi-continuous data that iron-out" the too-frequent values into completely continuous data. We show that the transformed data maintain the properties of the original data but are suitable for standard analysis.

We are also interested in the effect of concurrency not only on the final price of an auction but also on the relationship between the current bid levels and high bids in simultaneous ongoing auctions. We suggest several ways to visually represent the concurrent nature of online auction prices. These include ``rug plots" for displaying the price-evolution and price dynamics in concurrent auctions, time-grouped box plots, and moving statistics plots. We find price trends and relationships between prices in concurrent auctions and raise new research questions.

Finally, bids during an online auction arrive at unequally-spaced discrete time points. Our goal is to capture the entire continuous price-evolution function by representing it as a functional object. Various nonparametric smoothing methods exist to estimate the functional object from the observed discrete bid data. Previous studies use penalized polynomial and monotone smoothing splines; however, these require the determination of a large number of coefficients and often lengthy computational time. We present a family of parametric growth curves that describe the price-evolution during online auctions. Our approach is parsimonious and has an appealing interpretation in the online auction context. We also provide an automated fitting algorithm that is computationally fast.