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Odhadování na principu věrohodnosti
| Thesis title in Czech: | Odhadování na principu věrohodnosti |
|---|---|
| Thesis title in English: | Likelihood based estimation |
| Key words: | věrohodnost|maximální věrohodnost|psedo-věrohodnost|kvazi-věrohodnost |
| English key words: | likelihood|maximum likelihood|pseudo-likelihood|quasi-likelihood |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | čeština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Matúš Maciak, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 14.10.2022 |
| Date of assignment: | 14.10.2022 |
| Confirmed by Study dept. on: | 06.12.2022 |
| Date and time of defence: | 07.09.2023 09:00 |
| Date of electronic submission: | 20.07.2023 |
| Date of submission of printed version: | 24.07.2023 |
| Date of proceeded defence: | 07.09.2023 |
| Opponents: | Mgr. Ing. Pavel Kříž, Ph.D. |
| Guidelines |
| V určitom zmysle je matematická štatistika a štatistické metódy všeobecne postavená na probléme odhadovania neznámeho parametru (resp. neznámych parametrov).
K tomuto účelu slúži množstvo rôznych medód, postupov a algoritmov. Jedným z najdôležitejších je princím metódy maximálnej vierohodnosti. Cieľom práce je zoznámiť sa zo základmi metódy maximálnej vierohodnosti a s niektorými ďalšími modifikáciami odvodenými na základe vierohodnosti -- napr. kvázi-vierohodnosť, resp. pseudo-vierohodnosť. |
| References |
| [1] Cox, D.R. and Reid, N. (2004). "A note on pseudo-likelihood constructed from marginal densities". Biometrika. 91 (3): 729–737.
[2] Nedler, J. A. and Lee, Y. (1992). "Likelihood, Quasi-Likelihood and Pseudolikelihood: Some Comparisons". Journal of the Royal Statistical Society. Series B (Methodological), 54 (1): 273-284. [3] Varin, C. and Vidoni, P. (2005). "A note on composite likelihood inference and model selection" (PDF). Biometrika. 92 (3): 519–528. |
| Preliminary scope of work in English |
| One of the most important techniques commonly used in mathematical statistics for an estimation of unknown parameters is the maximum likelihood estimation method.
However, beside the method itself, there are also some important generalizations which usually aim at some assumptions being relaxed for better practical utilization. The idea of this thesis is to get familiar with the maximum likelihood method firstly and, later, to introduce some typical generalizations -- such as the quasi-likelihood method, respectively the pseudo-likelihood method. |