Množiny nejmenšího objemu
| Thesis title in Czech: | Množiny nejmenšího objemu |
|---|---|
| Thesis title in English: | Minimum volume sets |
| Key words: | odhadováni hustoty|množina minimálního objemu|úrovňová množina|elipsoid nejmenšího objemu |
| English key words: | density estimation|minimum volume set|level set|minimum volume ellipsoid |
| Academic year of topic announcement: | 2025/2026 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. Mgr. Stanislav Nagy, Ph.D. |
| Author: |
| Guidelines |
| Riešiteľ(ka) naštuduje a prehľadne spracuje základy problematiky odhadovania množín najmenšieho objemu s danou pravdepodobnosťou. Bude diskutovaný vzťah tohto problému s odhadmi úrovňových množín hustoty rozdelenia, a prístup bude porovnaný s konštrukciou optimálneho Neymanovho-Pearsonovho testu. |
| References |
| Van Aelst, S. and Rousseeuw, P. (2009). Minimum volume ellipsoid. WIREs Comp Stat, 1: 71-82.
Polonik, W. (1995). Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach. Ann. Statist. 23 (3) 855 - 881. Polonik, W. (1997). Minimum volume sets and generalized quantile processes. Stochastic Processes and their Applications, 69(1), 1-24. Nolan, D. (1991). The excess-mass ellipsoid. Journal of Multivariate Analysis, 39(2), 348-371. Polonik, W. (1997). Minimum Volume Sets in Statistics: Recent Developments. Classification and Knowledge Organization, 187-195. Nagy, S. (2023). Mathematical Statistics 2. Section 3.1. https://www.karlin.mff.cuni.cz/~nagy/NMSA332/NMSA332.pdf |