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Modelling price paths in on-line auctions: smoothing sparse and unevenly sampled curves by using semiparametric mixed models


  • Florian Reithinger
  • Wolfgang Jank
  • Gerhard Tutz
  • Galit Shmueli


On-line auctions pose many challenges for the empirical researcher, one of which is the effective and reliable modelling of price paths. We propose a novel way of modelling price paths in eBay's on-line auctions by using functional data analysis. One of the practical challenges is that the functional objects are sampled only very sparsely and unevenly. Most approaches rely on smoothing to recover the underlying functional object from the data, which can be difficult if the data are irregularly distributed. We present a new approach that can overcome this challenge. The approach is based on the ideas of mixed models. Specifically, we propose a semiparametric mixed model with boosting to recover the functional object. As well as being able to handle sparse and unevenly distributed data, the model also results in conceptually more meaningful functional objects. In particular, we motivate our method within the framework of eBay's on-line auctions. On-line auctions produce monotonic increasing price curves that are often correlated across auctions. The semiparametric mixed model accounts for this correlation in a parsimonious way. It also manages to capture the underlying monotonic trend in the data without imposing model constraints. Our application shows that the resulting functional objects are conceptually more appealing. Moreover, when used to forecast the outcome of an on-line auction, our approach also results in more accurate price predictions compared with standard approaches. We illustrate our model on a set of 183 closed auctions for Palm M515 personal digital assistants. Copyright (c) 2008 Royal Statistical Society.

Suggested Citation

  • Florian Reithinger & Wolfgang Jank & Gerhard Tutz & Galit Shmueli, 2008. "Modelling price paths in on-line auctions: smoothing sparse and unevenly sampled curves by using semiparametric mixed models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 127-148.
  • Handle: RePEc:bla:jorssc:v:57:y:2008:i:2:p:127-148

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    References listed on IDEAS

    1. Fitzenberger, Bernd & Wilke, Ralf A., 2007. "New insights on unemployment duration and post unemployment earnings in Germany: censored Box-Cox quantile regression at work," ZEW Discussion Papers 07-007, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    2. Koenker R. & Geling O., 2001. "Reappraising Medfly Longevity: A Quantile Regression Survival Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 458-468, June.
    3. Martin Biewen & Ralf Wilke, 2005. "Unemployment duration and the length of entitlement periods for unemployment benefits: do the IAB employment subsample and the German Socio-Economic Panel yield the same results?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(2), pages 209-236, June.
    4. Bernd Fitzenberger & Ralf A. Wilke, 2010. "Unemployment Durations in West Germany Before and After the Reform of the Unemployment Compensation System during the 1980s," German Economic Review, Verein für Socialpolitik, vol. 11, pages 336-366, August.
    5. Bernd Fitzenberger & Ralf Wilke, 2006. "Using quantile regression for duration analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 105-120, March.
    6. Dabrowska, D. M., 1995. "Nonparametric Regression with Censored Covariates," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 253-283, August.
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    Cited by:

    1. Matilde Trevisani & Arjuna Tuzzi, 2015. "A portrait of JASA: the History of Statistics through analysis of keyword counts in an early scientific journal," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1287-1304, May.
    2. Wolfgang Jank & Galit Shmueli & Shu Zhang, 2010. "A flexible model for estimating price dynamics in on-line auctions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 781-804.

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