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