Prípustnosť a neprípustnosť odhadu
| Thesis title in thesis language (Slovak): | Prípustnosť a neprípustnosť odhadu |
|---|---|
| Thesis title in Czech: | Přípustnost a nepřípustnost odhadu |
| Thesis title in English: | Admissibility and Inadmissibility of an Estimate |
| Key words: | Prípustnosť|Steinov odhad|stredná kvadratická odchýlka|odhad parametra |
| English key words: | Admissibility|Stein's estimate|mean squared error|parameter estimate |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | slovenština |
| 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: | 12.10.2022 |
| Date of assignment: | 13.10.2022 |
| Confirmed by Study dept. on: | 29.11.2022 |
| Date and time of defence: | 08.09.2023 08:20 |
| Date of electronic submission: | 20.07.2023 |
| Date of submission of printed version: | 24.07.2023 |
| Date of proceeded defence: | 08.09.2023 |
| Opponents: | prof. RNDr. Jana Jurečková, DrSc. |
| Guidelines |
| Kvalita odhadu parametru se často posuzuje pomoci střední čtvercové chyby (MSE). Při jednorozměrném parametru je odhad konstruován pomoci nejmenších čtverců také nejlepší.
Avšak při odhadování více než dvourozměrného parametru se odhad stane nepřípustný - resp. existuje jiný odhad, který je vzhledem k MSE pořád lepší než MSE odhad, nezávisle na hodnotě parametru. Tento poněkud překvapivý závěr je známy jako James Stein paradox. Cílem bakalářské práce je popsat přípustnost a nepřípustnost odhadu, definovat James Steinův odhad a vyšetřit chováni různých odhadů pomoci simulaci. |
| References |
| [1] Stein, C. (1956), Inadmissibility of the usual estimator for the mean of a multivariate distribution, Proc. Third Berkeley Symp. Math. Statist. Prob., 1, pp. 197–206.
[2] Stein, C. (1964), Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean, Annals of the Institute of Statistical Mathematics, Vol. 16, Issue 1, pp. 155–160. [3] Stein, C. (1981), Estimation of the Mean of a Multivariate Normal Distribution, The Annals of Statistics Vol. 9, No. 6, pp. 1135-1151. |
| Preliminary scope of work in English |
| The quality of some parameter estimate is usually assessed using the mean squared error risk (MSE). For one dimensional parameter, which is constructed by minimizing least squares, it is common that such estimate is the best with respect to MSE. However, for a vector parameter with more than two dimensions there is always some alternative estimator which always dominates the least squares estimate. This phenomenon is well known as the Stein Paradox.
The aim of the thesis is to describe admissibility and inadmissibility of the estimate (estimator) and to define James Stein estimate which, on the other hand, always dominates the least squares estimate one the parameter dimension is three or more. Simulation study should be used to compare different estimators. |