Nonparametric Inference of Utilites

Doctoral Thesis / Dissertation from the year 2006 in the subject Business economics - Marketing, Corporate Communication, CRM, Market Research, Social Media, grade: 1,0, Leipzig Graduate School of Management (Betriebswirtschaft), language: English, abstract: Inhaltsangabe:Abstract:§In Chapter 2, Foundations , we provide a description of selected parts of theories which we believe are helpful to better understand the contribution of this thesis. We start with the presentation of several behavioral hypotheses in preference and utility theory. Next, we describe the basics of inferential statistics and Conjoint Analysis. Then, we describe probabilistic entropy, in addition to that a later established version of it, and its axiomatization as a general inference principle. We conclude Chapter 2 by presenting La Mura's decision-theoretic entropy, a version of entropy as an inference technique for expected utilities. La Mura had developed this connection between probabilistic entropy and expected utilities in his Ph.D. thesis.§Based on his work, the initial research objective for this dissertation had been to make his approach applicable to the inference of unique consumer utilities given some observed evidence, having in mind the vast amounts of data that nowadays are available to analysts but still not used very effectively, in order to jointly overcome the limitations of Conjoint Analysis as mentioned above.§In the following five chapters you will see that our research has instead resulted in a new method, namely Entropy Analysis, which is not based on expected utility functions but on ordinary utility functions. We close Chapter 2 with a conclusion for the following chapters.§In Chapter 3, Entropy Analysis , we derive the new method combining probabilistic cross-entropy and ordinary utility functions. We start by imposing a set of conditions on the inference method. Then, we suggest a normalization of utility functions such that they become formally a probability measure. Finally, we present and prove our main result.§In Chapter 4, Irrational Behavior , we present a solution for the problem of how to treat observed irrational behavior (see Definition 4.1) with Entropy Analysis. This is motivated by two reasons. First, we are hardly able to observe perfectly rational data in any survey or for any given set of transaction data. Therefore, any utility inference method that cannot deal with irrational data will not be meaningful for research or commercial applications.§Second, our method is at first sight formally structured in a way in which its application to irrational data would return an inferred utility function that is trivial, i.e. uniform (to be further explained at the beginning of the chapter).§Our solution to this problem involves the principled use of a specific version of our method which we call relative Entropy Analysis, the cross-entropy version of Entropy Analysis. We start the chapter by presenting our general technique. Next, we substantiate our technique by suggesting one widely applicable heuristic.§In Chapter 5, Consumer Choice Models , we develop three consumer choice models to apply our method to marketing problems. We start by developing a basic model for consumer choices in which we consider preferences that relate product characteristics or bundles of goods with money.§Next, we constrain this basic model by imposing conditions on preference relations which imply utilities that are quasi-linear in money. We do this because such utilities reduce technical complexity for utility inference problems and because we believe that quasi-linear utilities (which imply the absence of income effects) are sufficiently representative for all items that have relatively low prices. Our third choice model uses von Neumann-Morgenstern expected utilities to apply our method to inference of utilities over risky alternatives.§I...