Dijkstra, Ysbrand (2021) Relation between empirical processes and Z/M-estimation. Bachelor's Thesis, Mathematics.
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Abstract
From the 1930's onward, the empirical processes theory is becoming more significant. Applications of empirical processes have led to great findings in non-parametric asymptotic statistics. Function classes can be called Glivenko-Cantelli if it satisfies properties like finite entropy and the envelope condition. Entropy plays also a huge role in least square estimation. Combined with other properties entropy can be used to prove consistency of the least square estimator and establish the rate of convergence. The reach of the empirical process theory goes further than M-estimation by effecting Z-estimation. With the usage of P-Donsker classes, asymptotic normality of Z-estimators can be established. With these applications of the empirical process theory in Z- and M-estimation, it is shown how influenceable this theory can be on non-parametric models.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Krijnen, W.P. and Grzegorczyk, M.A. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 11 Aug 2021 14:44 |
| Last Modified: | 11 Aug 2021 14:44 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/25660 |
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