Functional Data Analysis in Electronic Commerce Research

This paper describes opportunities and challenges of using functional data analysis (FDA) for the exploration and analysis of data originating from electronic commerce (eCommerce). We discuss the special data structures that arise in the online environment and why FDA is a natural approach for representing and analyzing such data. The paper reviews several FDA methods and motivates their usefulness in eCommerce research by providing a glimpse into new domain insights that they allow. We argue that the wedding of eCommerce with FDA leads to innovations both in statistical methodology, due to the challenges and complications that arise in eCommerce data, and in online research, by being able to ask (and subsequently answer) new research questions that classical statistical methods are not able to address, and also by expanding on research questions beyond the ones traditionally asked in the offline environment. We describe several applications originating from online transactions which are new to the statistics literature, and point out statistical challenges accompanied by some solutions. We also discuss some promising future directions for joint research efforts between researchers in eCommerce and statistics.Comment: Published at http://dx.doi.org/10.1214/088342306000000132 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Special Issue on Statistical Challenges and Opportunities in Electronic Commerce Research

This special issue is a product of the First Interdisciplinary Symposium on Statistical Challenges and Opportunities in Electronic Commerce Research, which took place on May 22--23, 2005, at the Robert H. Smith School of Business, University of Maryland, College Park (\url{www.smith.umd.edu/dit/statschallenges/}). The symposium brought together, for the first time, researchers from statistics, information systems, and related fields, all of whom work or are interested in empirical research related to electronic commerce. The goal of the symposium was to cross the borders, discuss joint research opportunities, expose this field and its statistical challenges, and promote collaboration between the different fields.Comment: Published at http://dx.doi.org/10.1214/088342306000000178 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A flexible regression model for count data

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive to Poisson regression. We propose a regression model based on the Conway--Maxwell-Poisson (COM-Poisson) distribution to address this problem. The COM-Poisson regression generalizes the well-known Poisson and logistic regression models, and is suitable for fitting count data with a wide range of dispersion levels. With a GLM approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a COM-Poisson regression over a standard Poisson regression. We compare the COM-Poisson to several alternatives and illustrate its advantages and usefulness using three data sets with varying dispersion.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS306 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The BARISTA: A model for bid arrivals in online auctions

The arrival process of bidders and bids in online auctions is important for studying and modeling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson bidder arrival process is a reasonable approximation. This approximation underlies theoretical derivations, statistical models and simulations used in field studies. However, when it comes to the bid arrivals, empirical research has shown that the process is far from Poisson, with early bidding and last-moment bids taking place. An additional feature that has been reported by various authors is an apparent self-similarity in the bid arrival process. Despite the wide evidence for the changing bidding intensities and the self-similarity, there has been no rigorous attempt at developing a model that adequately approximates bid arrivals and accounts for these features. The goal of this paper is to introduce a family of distributions that well-approximate the bid time distribution in hard-close auctions. We call this the BARISTA process (Bid ARrivals In STAges) because of its ability to generate different intensities at different stages. We describe the properties of this model, show how to simulate bid arrivals from it, and how to use it for estimation and inference. We illustrate its power and usefulness by fitting simulated and real data from eBay.com. Finally, we show how a Poisson bidder arrival process relates to a BARISTA bid arrival process.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS117 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

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