Selection criteria for copula-based dependence models
| Thesis title in Czech: | Informační kritéria pro výběr modelu založeného na kopulích |
|---|---|
| Thesis title in English: | Selection criteria for copula-based dependence models |
| Key words: | Akaikeho informační kritérium|informační kritéria|kopule|kopulové informační kritérium|pseudo-věrohodnost |
| English key words: | Akaike information criterion|copula|copula information criterion|information criteria|pseudo-likelihood |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. Ing. Marek Omelka, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 28.05.2024 |
| Date of assignment: | 28.05.2024 |
| Confirmed by Study dept. on: | 28.05.2024 |
| Date and time of defence: | 08.09.2025 00:00 |
| Date of electronic submission: | 17.07.2025 |
| Opponents: | doc. RNDr. Šárka Hudecová, Ph.D. |
| Advisors: | Johana Nešlehová |
| Christian Genest | |
| Guidelines |
| The student will first review various criteria for model selection, such as the Akaike and Bayesian information criteria, Kullback—Leibler information criterion, and Takeuchi information criterion, and explore their connections with cross validation and prediction error estimation. Focussing on copula-based dependence models, the student will further investigate the recently proposed copula information criterion and add theoretical results that demonstrate why the Akaike information criterion fails when rank-based pseudo-maximum likelihood estimation is used. A possible extension of the copula information criterion for copula models for discrete data will then be considered. Selected methods will be illustrated through a small-scale simulation study or on real data.
The student will work on the topic together with Johanna G, Nešlehová and Christian Genest (McGill University). That is why the assumed language of the thesis is English. |
| References |
| G. Claeskens and N. L. Hjort, Model Selection and Model Averaging, Cambridge University Press, 2008
S. Grønneberg and N. L. Hjort, The Copula Information Criteria, Scandinavian Journal of Statistics, 41 (2), 2014, pp. 436-459 L. A. Jordanger, and D. Tjøstheim. Model selection of copulas: AIC versus a cross validation copula information criterion. Statistics & Probability Letters, 92, 2014, 249–255. |