Fabric-diagram contour precision and size of counting element related to sample size by approximation theory methods |
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| Authors: | H Schaeben |
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| Institution: | (1) Lehr- and Forschungsgebiet Mineralogie und Gefügekunde, RWTH Aachen, Templergraben 55, 5100 Aachen, BRD |
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| Abstract: | Density estimation on the unit sphere by kernel methods may be conceived as a process of approximation by singular integrals. This concept aids in the solution of the main problems concerning the contouring of fabric diagrams. The optimal size of the counting element in Schmidt's method with respect to the mean integrated square error (MISE)of the density estimation is given. It proved that the optimal size is not only a function of the sample size but seriously depends on the smoothness of the density of directions on the sphere. In the light of approximation theory the Schmidt method of contouring is qualified as a moving average process; an example of a more refined density estimator is given. |
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| Keywords: | approximation singular integrals density estimation kernel methods contouring of fabric diagrams precision of density diagrams |
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