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Extremal Behaviour, Weak Convergence and Argmax Theory for a Class of Non-Stationary Marked Point Processes
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We formulate a random utility model where we choose from n options1; ; n. The options have associated independent and identicallydistributed (i.i.d) random variables fXi;Uigni=1, where Xi arethe characteristics of option i and Ui is its associated utility.We use the connection between point processes and extreme valuetheory to analyze the statistical properties of choice characteristics Xof the object with the highest utility as n ! 1. We derive analyticexpressions of the asymptotic distribution of choice characteristics fora range of distributional assumptions on the utilities Ui.In our discussion section, we suggest an extension of our method toallow us to further relax our distributional assumptions. We also showhow our theoretical model can be used to explain empirical patternsrelating to commuting time distributions.

National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-90159OAI: oai:DiVA.org:su-90159DiVA: diva2:623285
Available from: 2013-05-27 Created: 2013-05-27 Last updated: 2013-06-03
In thesis
1. Random Choice over a Continuous Set of Options
Open this publication in new window or tab >>Random Choice over a Continuous Set of Options
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Random choice theory has traditionally modeled choices over a -nite number of options. This thesis generalizes the literature by studyingthe limiting behavior of choice models as the number of optionsapproach a continuum.The thesis uses the theory of random elds, extreme value theoryand point processes to calculate this limiting behavior. For a numberof distributional assumptions, we can give analytic expressions forthe limiting probability distribution of the characteristics of the bestchoice. In addition, we also outline a straightforward extension to ourtheory which would signicantly relax the distributional assumptionsneeded to derive analytical results.Some examples from commuting research are discussed to illustratepotential applications of the theory.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2013. 65 p.
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-89917 (URN)
Presentation
2013-06-05, Rum 5:306 Matematiska Institutionen, Kräftriket, Stockholm, 15:00 (English)
Supervisors
Available from: 2013-05-22 Created: 2013-05-15 Last updated: 2013-06-03Bibliographically approved

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Malmberg, Hannes
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