Halfspace depth for location and scatter: robustness and minimax optimality
| Thesis title in Czech: | Poloprostorová hloubka lokace a disperze: robustnost a minimax optimalita |
|---|---|
| Thesis title in English: | Halfspace depth for location and scatter: robustness and minimax optimality |
| Key words: | vícerozměrná analýza|poloprostorová hloubka|poloprostorová hloubka disperze|robustnost|minimax optimalita |
| English key words: | multivariate analysis|halfspace depth|scatter halfspace depth|robustness|minimax optimality |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. Mgr. Stanislav Nagy, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 16.10.2023 |
| Date of assignment: | 18.10.2023 |
| Confirmed by Study dept. on: | 18.10.2023 |
| Date and time of defence: | 05.09.2024 09:10 |
| Date of electronic submission: | 18.07.2024 |
| Date of submission of printed version: | 18.07.2024 |
| Date of proceeded defence: | 05.09.2024 |
| Opponents: | doc. RNDr. Daniel Hlubinka, Ph.D. |
| Guidelines |
| Riešiteľ popíše a porovná klasickú polopriestorovú hĺbku pre viacrozmerné dáta s jej variantou pre disperzné matice náhodných vektorov. Príslušné koncepty mediánu budú vyšetrované z hľadiska robustnosti. |
| References |
| Donoho, D. L. and Gasko, M. (1992). Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Ann. Stat. 20 1803–1827.
D. Paindaveine, G. Van Bever (2018). Halfspace depths for scatter, concentration and shape matrices. Ann. Stat. 46, 3276–3307. M. Chen, C. Gao, Z. Ren (2018). Robust covariance and scatter matrix estimation under Huber’s contamination model. Ann. Stat. 46, 1932–1960. |