Principal component decomposition of non-parametric tests |
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Authors: | Arnold Janssen |
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Institution: | (1) Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany |
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Abstract: | Summary Let denote an arbitrary non-parametric unbiased test for a Gaussian shift given by an infinite dimensional parameter space. Then it is shown that the curvature of its power function has a principal component decomposition based on a Hilbert-Schmidt operator. Thus every test has reasonable curvature only for a finite number of orthogonal directions of alternatives. As application the two-sided Kolmogorov-Smirnov goodnessof-fit test is treated. We obtain lower bounds for their local asymptotic relative efficiency. They converge to one as 0 for the directionh
0(u)=sign(2u–1) of the gradient of the median test. These results are analogous to earlier results of Hájek and idák for one-sided Kolmogorov-Smirnov tests. |
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Keywords: | 62G10 62G20 |
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