Robuste Schätzung durch Approximation von Matrizen niedrigen Ranges

Abstract

In this thesis is discussed whether the theory of low rank decomposition (LRD) can be used for creating robust estimators. Therefore, robust location estimation and robust covariance estimation is used. In a first section particular frame conditions for each experiment are set up for creating a synthetic data matrix. The output of decomposing this matrix is a low ranked matrix free from errors and a sparse error matrix containing all detected errors. By analyzing those two matrices a weighting factor can be determined. Aspects are robustness, the quality of location and covariance estimation and a high accuracy at detecting outliers. An appropriate and well-fitting weighting factor is used in a second block of experiments. Low rank decomposition is compared to other estimators such as robust minimum covariance determinant (MCD) and the arithmetic mean. Good results at using the low rank decomposition are achieved when choosing an appropriate weighting factor and with good information about the given data. Nevertheless, is it very important to keep in mind that the weighting factor can have a very big influence on the parameter estimation.