Essays on Some Recent Penalization Methods with Applications in Finance and Marketing

The subject of this PhD research is within the areas of Econometrics and Artificial Intelligence. More concretely, it deals with the tasks of statistical regression and classification analysis. New classification methods have been proposed, as well as new applications of established ones in the areas of Finance and Marketing. The bulk of this PhD research centers on extending standard methods that fall under the general term of loss-versus-penalty classification techniques. These techniques build on the premises that a model that uses a finite amount of available data to be trained on should neither be too complex nor too simple in order to possess a good forecasting ability. New proposed classification techniques in this area are Support Hyperplanes, Nearest Convex Hull classification and Soft Nearest Neighbor. Next to the new techniques, new applications of some standard loss-versus-penalty methods have been put forward. Specifically, these are the application of the so-called Support Vector Machines (SVMs) for classification and regression analysis to financial time series forecasting, solving the Market Share Attraction model and solving and interpreting binary classification tasks in Marketing. In addition, this research focuses on new efficient solutions to SVMs using the so-called majorization algorithm. This algorithm provides for the possibility to incorporate various so-called loss functions while solving general SVM-like methods

Instance-Based penalization techniques for classification

Several instance-based large-margin classi¯ers have recently been put forward in the literature: Support Hyperplanes, Nearest Convex Hull classifier, and Soft Nearest Neighbor. We examine those techniques from a common fit-versus-complexity framework and study the links be- tween them. Finally, we compare the performance of these techniques vis-a-vis each other and other standard classification methods

Nearest convex hull classification

Consider the classification task of assigning a test object to one of two or more possible groups, or classes. An intuitive way to proceed is to assign the object to that class, to which the distance is minimal. As a distance measure to a class, we propose here to use the distance to the convex hull of that class. Hence the name Nearest Convex Hull (NCH) classification for the method. Convex-hull overlap is handled through the introduction of slack variables and kernels. In spirit and computationally the method is therefore close to the popular Support Vector Machine (SVM) classifier. Advantages of the NCH classifier are its robustness to outliers, good regularization properties and relatively easy handling of multi-class problems. We compare the performance of NCH against state-of-art techniques and report promising results

Solving and interpreting binary classification problems in marketing with SVMs

Marketing problems often involve inary classification of customers into ``buyers'' versus ``non-buyers'' or ``prefers brand A'' versus ``prefers brand B''. These cases require binary classification models such as logistic regression, linear, and quadratic discriminant analysis. A promising recent technique for the binary classification problem is the Support Vector Machine (Vapnik (1995)), which has achieved outstanding results in areas ranging from Bioinformatics to Finance. In this paper, we compare the performance of the Support Vector Machine against standard binary classification techniques on a marketing data set and elaborate on the interpretation of the obtained results

SVM-Maj: a majorization approach to linear support vector machines with different hinge errors

Support vector machines (SVM) are becoming increasingly popular for the prediction of a binary dependent variable. SVMs perform very well with respect to competing techniques. Often, the solution of an SVM is obtained by switching to the dual. In this paper, we stick to the primal support vector machine (SVM) problem, study its effective aspects, and propose varieties of convex loss functions such as the standard for SVM with the absolute hinge error as well as the quadratic hinge and the Huber hinge errors. We present an iterative majorization algorithm that minimizes each of the adaptations. In addition, we show that many of the features of an SVM are also obtained by an optimal scaling approach to regression. We illustrate this with an example from the literature and do a comparison of different methods on several empirical data sets

Nonlinear support vector machines through iterative majorization and I-splines

To minimize the primal support vector machine (SVM) problem, we propose to use iterative majorization. To do so, we propose to use it- erative majorization. To allow for nonlinearity of the predictors, we use (non)monotone spline transformations. An advantage over the usual ker- nel approach in the dual problem is that the variables can be easily inter- preted. We illustrate this with an example from the literature

Estimating the market share attraction model using support vector regressions.

We propose to estimate the parameters of the Market Share Attraction Model (Cooper & Nakanishi, 1988; Fok & Franses, 2004) in a novel way by using a non-parametric technique for function estimation called Support Vector Regressions (SVR) (Vapnik, 1995; Smola, 1996). 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, ML 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 over¯tting. This kind of estimation forms the basis of the SVR technique, which, as we will argue, makes it a good candidate for solving 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 stronger results than when using a ML estimation procedure

A prospective study comparing the predictions of doctors versus models for treatment outcome of lung cancer patients: A step toward individualized care and shared decision making

Background: Decision Support Systems, based on statistical prediction models, have the potential to change the way medicine is being practiced, but their application is currently hampered by the astonishing lack of impact studies. Showing the theoretical benefit of using these models could stimulate conductance of such studies. In addition, it would pave the way for developing more advanced models, based on genomics, proteomics and imaging information, to further improve the performance of the models. Purpose: In this prospective single-center study, previously developed and validated statistical models were used to predict the two-year survival (2yrS), dyspnea (DPN), and dysphagia (DPH) outcomes for lung cancer patients treated with chemo radiation. These predictions were compared to probabilities provided by doctors and guideline-based recommendations currently used. We hypothesized that model predictions would significantly outperform predictions from doctors. Materials and methods: Experienced radiation oncologists (ROs) predicted all outcomes at two timepoints: (1) after the first consultation of the patient, and (2) after the radiation treatment plan was made. Differences in the performances of doctors and models were assessed using Area Under the Curve (AUC) analysis. Results: A total number of 155 patients were included. At timepoint #1 the differences in AUCs between the ROs and the models were 0.15, 0.17, and 0.20 (for 2yrS, DPN, and DPH, respectively), with p-values of 0.02, 0.07, and 0.03. Comparable differences at timepoint #2 were not statistically significant due to the limited number of patients. Comparison to guideline-based recommendations also favored the models. Conclusion: The models substantially outperformed ROs' predictions and guideline-based recommendations currently used in clinical practice. Identification of risk groups on the basis of the models facilitates individualized treatment, and should be further investigated in clinical impact studies