This study compares the performance of the Maximum Likelihood estimator (MLE), estimators based on spacings called Generalized Maximum Spacing estimators (GSEs), and the One Step Minimum Hellinger Distance estimator (OSMHD), on data originating from a circular distribution. The purpose of the study is to investigate the different estimators’ performance on directional data. More specifically, we compare the estimators’ ability to estimate parameters of the von Mises distribution, which is determined by a location parameter and a scale parameter. For this study, we only look at the scenario in which one of the parameters is unknown. The main part of the study is concerned with estimating the parameters under the condition, in which the data contain outliers, but a small part is also dedicated to estimation at the true model. When estimating the location parameter under contaminated conditions, the results indicate that some versions of the GSEs tend to outperform the other estimators. It should be noted that these seemingly more robust estimators appear comparatively less optimal at the true model, but this is a tradeoff that must be made on a case by case basis. Under the same contaminated conditions, all included estimators appear to have seemingly greater difficulties estimating the scale parameter. However, for this case, some of the GSEs are able to handle the contamination a bit better than the rest. In addition, there might exist other versions of GSEs, not included in this study, which perform better.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:umu-149426 |
| Date | January 2018 |
| Creators | Brännström, Anton |
| Publisher | Umeå universitet, Statistik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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