Finite sensibility and utility functions

According to the concept of finite sensibility an individual utility function has to fulfill Ng's (1975) Convention 1. In this paper we show that relatively weak assumptions already guarantee the existence of a utility function with the desired property and we present a procedure for constructing such a utility function.     

Intensive gamblers on German-style slot-machines

Results of German-style slot-machine gambling are reported, stemming from seven individual surveys in representatively sampled households (N=7,643). The aim of the inquiry was the reexamination of studies of the number of gamblers in the population together with gambling hours spent per week by active gamblers. The results are largely identical with already known data. Of persons of voting age or older, 10.2% are active gamblers (4.6 million; having gambled at least once within the last 3 months). Of the active gamblers 0.7% are intensive gamblers (5 hours and more per week). These persons number approximately 32,000 in the Federal Republic of Germany, or from 12,000 to 71,000 (95% confidence interval). In addition to the frequency distributions, interactions with socio-demographic characteristics were examined, and an estimate was made for the prevalence of intensive gamblers with severe stress.This article was first published in Germany: Bühringer, G. & Konstanty, R., (1989) Vielsspieler an Geldautomaten in der Bundesrepublik Deutschland, Suchtgefahren 35, 1–13.     

Using Analysis of Variance and Factor Analysis for the Reduction of High Dimensional Variation in Time Series of Energy Consumption

Summary: In this paper the complexity of high dimensional data with cyclical variation is reduced using analysis of variance and factor analysis. It is shown that the prediction of a small number of main cyclical factors is more useful than forecasting all the time-points separately as it is usually done by seasonal time series models. To give an example for this approach we analyze the electricity demand per quarter of an hour of industrial customers in Germany. The necessity of such predictions results from the liberalization of the German electricity market in 1998 due to legal requirements of the EC in 1996.     

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

Summary.  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.     

A comparison of methods for the fitting of generalized additive models

There are several procedures for fitting generalized additive models, i.e. regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data are used to compare a smoothing parameter optimization approach for selection of smoothness and of covariates, a stepwise approach, a mixed model approach, and a procedure based on boosting techniques. In particular it is investigated how the performance of procedures is linked to amount of information, type of response, total number of covariates, number of influential covariates, and extent of non-linearity. Measures for comparison are prediction performance, identification of influential covariates, and smoothness of fitted functions. One result is that the mixed model approach returns sparse fits with frequently over-smoothed functions, while the functions are less smooth for the boosting approach and variable selection is less strict. The other approaches are in between with respect to these measures. The boosting procedure is seen to perform very well when little information is available and/or when a large number of covariates is to be investigated. It is somewhat surprising that in scenarios with low information the fitting of a linear model, even with stepwise variable selection, has not much advantage over the fitting of an additive model when the true underlying structure is linear. In cases with more information the prediction performance of all procedures is very similar. So, in difficult data situations the boosting approach can be recommended, in others the procedures can be chosen conditional on the aim of the analysis.     

Improved nearest neighbor classifiers by weighting and selection of predictors

Nearest neighborhood classification is a flexible classification method that works under weak assumptions. The basic concept is to use the weighted or un-weighted sums over class indicators of observations in the neighborhood of the target value. Two modifications that improve the performance are considered here. Firstly, instead of using weights that are solely determined by the distances we estimate the weights by use of a logit model. By using a selection procedure like lasso or boosting the relevant nearest neighbors are automatically selected. Based on the concept of estimation and selection, in the second step, we extend the predictor space. We include nearest neighborhood counts, but also the original predictors themselves and nearest neighborhood counts that use distances in sub dimensions of the predictor space. The resulting classifiers combine the strength of nearest neighbor methods with parametric approaches and by use of sub dimensions are able to select the relevant features. Simulations and real data sets demonstrate that the method yields better misclassification rates than currently available nearest neighborhood methods and is a strong and flexible competitor in classification problems.