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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Exploiting numerical linear algebra to accelerate the computation of the MCD estimator
 Sommerová, Kristýna ; Duintjer Tebbens, Erik Jurjen (advisor) ; Hnětynková, Iveta (referee)
This work is dealing with speeding up the algorithmization of the MCD es- timator for detection of the mean and the covariance matrix of a normally dis- tributed multivariate data contaminated with outliers. First, the main idea of the estimator and its well-known aproximation by the FastMCD algorithm is discussed. The main focus was to be placed on possibilities of a speedup of the iteration step known as C-step while maintaining the quality of the estimations. This proved to be problematic, if not impossible. The work is, therefore, aiming at creating a new implementation based on the C-step and Jacobi method for eigenvalues. The proposed JacobiMCD algorithm is compared to the FastMCD in terms of floating operation count and results. In conclusion, JacobiMCD is not found to be fully equivalent to FastMCD but hints at a possibility of its usage on larger problems. The numerical experiments suggest that the computation can indeed be quicker by an order of magnitude, while the quality of results is close to those from FastMCD in some settings. 1
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Computation and applications of the MCD estimator for robust statistical analysis
 Sommerová, Kristýna ; Duintjer Tebbens, Erik Jurjen (advisor) ; Hnětynková, Iveta (referee)
This work describes one of the basic problems of robust statistics con- cerning outlier detection and its possible solution by using the Minimum covariance determinant estimator for estimates of the mean value and the covariance matrix with multivariate data. It explains how the estimator works and analyses its properties. The work concentrates on its approximation based on the fastMCD algorithm and specifies its numerical properties with emphasis on computational costs and stability of the standard implementation in MATLAB. It also discusses possible modifications of the algorithm and its effects on numerical properties. Lastly the work shows the usage of the fastMCD algorithm on a few real data experiments. Powered by TCPDF (www.tcpdf.org)
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1 Sommerová, Katarína
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