Copula-based multivariate association measures and tail coefficients
| Thesis title in Czech: | Mnohorozměrné míry asociace a koeficienty závislosti chvostů založené na kopulích |
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| Thesis title in English: | Copula-based multivariate association measures and tail coefficients |
| Key words: | asymptotická normalita|konzistence|kopule|míra asociace|mnohorozměrná analýza|odhad|shlukování|závislost|závislost chvostů |
| English key words: | association measure|asymptotic normality|cluster analysis|consistency|copula|dependence|estimation|multivariate analysis|tail dependence |
| Academic year of topic announcement: | 2016/2017 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. Ing. Marek Omelka, Ph.D. |
| Author: | Mgr. Vojtěch Kika, Ph.D. - assigned and confirmed by the Study Dept. |
| Date of registration: | 20.09.2017 |
| Date of assignment: | 20.09.2017 |
| Confirmed by Study dept. on: | 21.11.2017 |
| Date and time of defence: | 10.09.2021 09:30 |
| Date of electronic submission: | 04.08.2021 |
| Date of submission of printed version: | 04.08.2021 |
| Date of proceeded defence: | 10.09.2021 |
| Opponents: | Noel Veraverbeke |
| Sebastian Fuchs | |
| Guidelines |
| Student(ka) se seznámí s metodami inference pro modely mnohorozměrných rozdělení, které využívají kopule. Zaměří se zejména na metody pro odhad kopule a na související statistické testy. Jako vhodné možnosti se jeví zejména odhad kopulí za přítomnosti vysvětlujících proměnných. Dále také pak výzkum vícerozměrných kopulí pro náhodné vektory s dimenzí větší než dva. Teoretické výsledky budou ilustrovány pomocí simulačních studií a aplikací na reálná data. |
| References |
| Genest, C., Nešlehová, J. and Ziegel, J. (2011). Inference in multivariate Archimedean copula models. Test, 20, 223–256.
Genest, C. and Rivest, L.: Statistical Inference Procedures for Bivariate Archimedean Copulas (1993). Journal of the American Statistical Association, 88, 1034–1043. Genest, C., Remillard, B., and Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics. 44, 199-213 Gijbels, I., Omelka, M., and Veraverbeke, N. (2015). Estimation of a copula when a covariate affects only marginal distributions. Scandinavian Journal of Statistics, 42, 1109–1126. Grothe, O., Schnieders, J. and Segers, J. (2014). Measuring association and dependence between random vectors. Journal of Multivariate Analysis, 123, 96–110. Joe, H. (2014). Dependence modeling with copulas. CRC Press. Nelsen, R.B.: An Introduction to Copulas, Second Edition, Springer-Verlag New York, Inc.; 2006. Schmid, F., Schmidt, R. Blumentritt, T., Gaisser, S. and Ruppert, M. (2010). Copula-based measures of multivariate association. In Copula Theory and Its Applications, Lecture Notes in Statistics, 198, Eds: P. Jaworski et al., Chapter 10. Tsukahara, H. (2005). Semiparametric estimation in copula models. Canadadian Journal of Statistics, 33, 357–375. |