Border estimation of a disc observed with random errors solved in two steps |
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Authors: | Kristian Sabo Mirta Benšić |
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Institution: | Department of Mathematics, University of Osijek, Gajev trg 6, HR-31 000 Osijek, Croatia |
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Abstract: | The problem of estimating the boundary of a uniform distribution on a disc is considered when data are measured with normally distributed additive random error. The problem is solved in two steps. In the first step the domain is subdivided into thin slices and the endpoints of slices are obtained within the framework of a corresponding one-dimensional problem. For the estimations implemented in that step the moment method and the maximum likelihood method are used. As there are numerical problems with calculating the variance of the estimator in the maximum likelihood approach, its good approximation is also given. |
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Keywords: | Maximum likelihood estimator Method of moments estimator Uniform distribution Weighted total least-squares circle fitting |
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