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vom Scheidt, J.; Starkloff, H.-J.; Wunderlich, R. : Optimal low-dimensional approximations of random vector functions

vom Scheidt, J.; Starkloff, H.-J.; Wunderlich, R. : Optimal low-dimensional approximations of random vector functions

Author(s) :
vom Scheidt, J.; Starkloff, H.-J.; Wunderlich, R.
Title :
Optimal low-dimensional approximations of random vector functions
Electronic source :
[gzipped dvi-file] 42 kB
[gzipped ps-file] 75 kB
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-31, 1998
Mathematics Subject Classification :
60G12 [ General second order processes ]
41A63 [ Multidimensional approximation problems ]
Abstract :
The paper considers approximations of first- and second-order moments of random functions with values in a high-dimensional Euclidean space using projections onto suitable low-dimensional linear submanifolds. To quantify the goodness of the approximation a criterion based on the mean squared Euclidean distance is introduced. In case of wide-sense stationary random functions optimal low-dimensional linear submanifolds are given in terms of the mean vector and eigenvectors of the variance matrix.
Keywords :
random vector process, low-dimensional approximation, optimal projection
Language :
english
Publication time :
12/1998