Smoothing sparse and unevenly sampled curves using semiparametric mixed models: an application to online auctions

Arbeitspapier

Functional data analysis can be challenging when 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 is irregularly distributed. In this paper 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. While the model can handle sparse and unevenly distributed data, it also results in conceptually more meaningful functional objects. In particular, we motivate our method within the framework of eBay's online auctions. Online auctions produce monotonic increasing price curves that are often correlated across two auctions. The semiparametric mixed model accounts for this correlation in a parsimonious way. It also estimates the underlying increasing trend from 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 online auction, our approach also results in more accurate price predictions compared to standard approaches. We illustrate our model on a set of 183 closed auctions for Palm M515 personal digital assistants.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 483

Classification and Topics

• Subject: Nonparametric methods ; smoothing ; mixed model ; boosting ; penalized splines ; online auction ; eBay

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Reithinger, Florian ; Jank, Wolfgang ; Tutz, Gerhard ; Shmueli, Galit
• Event: Veröffentlichung
• (who): Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
• (where): München
• (when): 2006

Further information

• DOI: doi:10.5282/ubm/epub.1851
• Handle: http://hdl.handle.net/10419/31032
• URN: urn:nbn:de:bvb:19-epub-1851-1
• Last update: 10.03.2025, 11:44 AM CET