Border estimation of a disc observed with random errors solved in two steps

Authors:
Kristian Sabo;Mirta Benšić
Affiliations:
Department of Mathematics, University of Osijek, Gajev trg 6, HR-31 000 Osijek, Croatia;Department of Mathematics, University of Osijek, Gajev trg 6, HR-31 000 Osijek, Croatia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Estimating the width of a uniform distribution when data are measured with additive normal errors with known variance

Computational Statistics & Data Analysis

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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. In the second step the obtained endpoints are used to estimate the boundary using the total least-squares curve fitting procedure. A necessary and sufficient condition for the existence of the total least-squares solution is also given. Finally, simulation results are presented.