http://repub.eur.nl/res/concept/jel-C45/ Recent publications classified by JEL Code C45 en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/21926/ 2010-09-01T00:00:00Z We propose to estimate the parameters of the Market Share Attraction Model (Cooper and Nakanishi, 1988; Fok and Franses, 2004) in a novel way by using a nonparametric technique for function estimation called Support Vector Regressions (SVR) (Smola, 1996; Vapnik, 1995). Traditionally, the parameters of the Market Share Attraction Model are estimated via a Maximum Likelihood (ML) procedure, assuming that the data are drawn from a conditional Gaussian distribution. However, if the distribution is unknown, Ordinary Least Squares (OLS) estimation may seriously fail (Vapnik, 1982). One way to tackle this problem is to introduce a linear loss function over the errors and a penalty on the magnitude of model coefficients. This leads to qualities such as robustness to outliers and avoidance of the problem of overfitting. This kind of estimation forms the basis of the SVR technique, which, as we will argue, makes it a good candidate for estimating the Market Share Attraction Model. We test the SVR approach to predict (the evolution of) the market shares of 36 car brands simultaneously and report promising results. Nalbantov, G.I. Franses, Ph.H.B.F. Groenen, P.J.F. Bioch, J.C. http://repub.eur.nl/res/pub/13675/ 2008-04-18T00:00:00Z Highly non-elliptical posterior distributions may occur in several econometric models, in particular, when the likelihood information is allowed to dominate and data information is weak. We explain the issue of highly non-elliptical posteriors in a model for the effect of education on income using data from the well-known Angrist and Krueger (1991) study and discuss how a so-called Information Matrix or Jeffreys' prior may be used as a `regularization prior' that in combination with the likelihood yields posteriors with desirable properties. We further consider an 8-dimensional bimodal posterior distribution in a 2-regime mixture model for the real US GNP growth. In order to perform a Bayesian posterior analysis using indirect sampling methods in these models, one has to find a good candidate density. In a recent paper - Hoogerheide, Kaashoek and Van Dijk (2007) - a class of neural network functions was introduced as candidate densities in case of non-elliptical posteriors. In the present paper, the connection between canonical model structures, non-elliptical credible sets, and more sophisticated neural network simulation techniques is explored. In all examples considered in this paper – a bimodal distribution of Gelman and Meng (1991) and posteriors in IV and mixture models - the mixture of Student's t distributions is clearly a much better candidate than a Student's t candidate, yielding far more precise estimates of posterior means after the same amount of computing time, whereas the Student's t candidate almost completely misses substantial parts of the parameter space. Hoogerheide, L.F. Dijk, H.K. van http://repub.eur.nl/res/pub/11158/ 2007-07-01T00:00:00Z Likelihoods and posteriors of instrumental variable (IV) regression models with strong endogeneity and/or weak instruments may exhibit rather non-elliptical contours in the parameter space. This may seriously affect inference based on Bayesian credible sets. When approximating posterior probabilities and marginal densities using Monte Carlo integration methods like importance sampling or Markov chain Monte Carlo procedures the speed of the algorithm and the quality of the results greatly depend on the choice of the importance or candidate density. Such a density has to be ‘close’ to the target density in order to yield accurate results with numerically efficient sampling. For this purpose we introduce neural networks which seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. A key step in the proposed class of methods is the construction of a neural network that approximates the target density. The methods are tested on a set of illustrative IV regression models. The results indicate the possible usefulness of the neural network approach. Hoogerheide, L.F. Kaashoek, J.F. Dijk, H.K. van http://repub.eur.nl/res/pub/10073/ 2007-04-24T00:00:00Z In this paper, a bibliometric study of the computational intelligence field is presented. Bibliometric maps showing the associations between the main concepts in the field are provided for the periods 1996–2000 and 2001–2005. Both the current structure of the field and the evolution of the field over the last decade are analyzed. In addition, a number of emerging areas in the field are identified. It turns out that computational intelligence can best be seen as a field that is structured around four important types of problems, namely control problems, classification problems, regression problems, and optimization problems. Within the computational intelligence field, the neural networks and fuzzy systems subfields are fairly intertwined, whereas the evolutionary computation subfield has a relatively independent position. Eck, N.J.P. van Waltman, L.R. http://repub.eur.nl/res/pub/2007/ 2005-03-31T00:00:00Z Likelihoods and posteriors of instrumental variable regression models with strong endogeneity and/or weak instruments may exhibit rather non-elliptical contours in the parameter space. This may seriously affect inference based on Bayesian credible sets. When approximating such contours using Monte Carlo integration methods like importance sampling or Markov chain Monte Carlo procedures the speed of the algorithm and the quality of the results greatly depend on the choice of the importance or candidate density. Such a density has to be `close' to the target density in order to yield accurate results with numerically efficient sampling. For this purpose we introduce neural networks which seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. A key step in the proposed class of methods is the construction of a neural network that approximates the target density accurately. The methods are tested on a set of illustrative models. The results indicate the feasibility of the neural network approach. Hoogerheide, L.F. Kaashoek, J.F. Dijk, H.K. van http://repub.eur.nl/res/pub/1281/ 2004-05-19T00:00:00Z Likelihoods and posteriors of econometric models with strong endogeneity and weak instruments may exhibit rather non-elliptical contours in the parameter space. This feature also holds for cointegration models when near non-stationarity occurs and determining the number of cointegrating relations is a nontrivial issue, and in mixture processes where the modes are relatively far apart. The performance of Monte Carlo integration methods like importance sampling or Markov Chain Monte Carlo procedures greatly depends in all these cases on the choice of the importance or candidate density. Such a density has to be `close' to the target density in order to yield numerically accurate results with efficient sampling. Neural networks seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. That is, conditionally upon the specification of the neural network, sampling can be done either directly or using a Gibbs sampling technique, possibly using auxiliary variables. A key step in the proposed class of methods is the construction of a neural network that approximates the target density accurately. The methods are tested on a set of illustrative models which include a mixture of normal distributions, a Bayesian instrumental variable regression problem with weak instruments and near non-identification, a cointegration model with near non-stationarity and a two-regime growth model for US recessions and expansions. These examples involve experiments with non-standard, non-elliptical posterior distributions. The results indicate the feasibility of the neural network approach. Hoogerheide, L.F. Kaashoek, J.F. Dijk, H.K. van http://repub.eur.nl/res/pub/323/ 2003-04-29T00:00:00Z For successful trading in financial markets, it is important to develop financial models where one can identify different states of the market for modifying one???s actions. In this paper, we propose to use probabilistic fuzzy systems for this purpose. We concentrate on Takagi???Sugeno (TS) probabilistic fuzzy systems that combine interpretability of fuzzy systems with the statistical properties of probabilistic systems. We start by recapitulating the general architecture of TS probabilistic fuzzy rule-based systems and summarize the corresponding reasoning schemes. We mention how probabilities can be estimated from a given data set and how a probability distribution can be approximated by a fuzzy histogram. We apply our methodology for financial time series analysis and demonstrate how a probabilistic TS fuzzy system can be identified, assuming that a linguistic term set is given. We illustrate the interpretability of such a system by inspecting the rule bases of our models. Berg, J. van den Bergh, W.M. van den Kaymak, U. http://repub.eur.nl/res/pub/1727/ 2002-12-31T00:00:00Z The performance of Monte Carlo integration methods like importance sampling or Markov Chain Monte Carlo procedures greatly depends on the choice of the importance or candidate density. Usually, such a density has to be "close" to the target density in order to yield numerically accurate results with efficient sampling. Neural networks seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. That is, conditional upon the specification of the neural network, sampling can be done either directly or using a Gibbs sampling technique, possibly using auxiliary variables. A key step in the proposed class of methods is the construction of a neural network that approximates the target density accurately. The methods are tested on a set of illustrative models which include a mixture of normal distributions, a Bayesian instrumental variable regression problem with weak instruments and near-identification, and two-regime growth model for US recessions and expansions. These examples involve experiments with non-standard, non-elliptical posterior distributions. The results indicate the feasibility of the neural network approach. Hoogerheide, L.F. Kaashoek, J.F. Dijk, H.K. van http://repub.eur.nl/res/pub/79/ 2001-03-20T00:00:00Z The concept of consideration sets makes brand choice a two-step process. House-holds first construct a consideration set which not necessarily includes all available brands and conditional on this set they make a final choice. In this paper we put forward a parametric econometric model for this two-step process, where we take into account that consideration sets usually are not observed. It turns out that our model is an artificial neural network, where the consideration set corresponds with the hidden layer. We discuss representation, parameter estimation and inference. We illustrate our model for the choice between six detergent brands and show that the model improves upon a one-step multinomial logit model, in terms of fit and out-of-sample forecasting. Vroomen, B.L.K. Franses, Ph.H.B.F. Nierop, J.E.M. van http://repub.eur.nl/res/pub/6932/ 2000-11-10T00:00:00Z In an oligopoly, prior to competing in the market, firms have an opportunity to form pair-wise collaborative links with other firms. These pair-wise links involve a commitment of resources and lead to lower costs of production of the collaborating firms. The collection of pair-wise links defines a collaboration network. We study the architecture of strategically stable networks. Our analysis reveals that in a setting where firms are ex-ante identical, strategically stable networks are often asymmetric, with some firms having a large number of links while others have few links or no links at all. We characterize such asymmetric networks; the dominant group architecture, stars, and inter-linked stars are found to be stable. In asymmetric networks, the firms with many links have lower costs of production as compared to firms with few links. Thus collaboration links can have a major influence on the functioning of the market. Goyal, S. Joshi, S.