Reweighted Smooth Tests of Goodness of Fit

Starting from a smooth test for goodness of fit we develop a method to alter this test to a reweighted smooth test, which has greater power to a certain directional alternative. Whereas the original smooth test gives equal weight to the different directions in the space of alternatives, the reweight...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2011-01, Vol.40 (9), p.1651-1670
Main Authors: De Boeck, B., Thas, O., Ottoy, J. P.
Format: Article
Language:English
Subjects:
62-02
Directional alternative
Distribution theory
Exact sciences and technology
Functional analysis
General topics
Goodness of fit
Hilbert space
Mathematical analysis
Mathematics
Orthonormal polynomials
Power
Probability and statistics
Sciences and techniques of general use
Score test
Smooth test
Statistics
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Summary:Starting from a smooth test for goodness of fit we develop a method to alter this test to a reweighted smooth test, which has greater power to a certain directional alternative. Whereas the original smooth test gives equal weight to the different directions in the space of alternatives, the reweighted smooth test makes a distinction in importance of the directions. The advantage of this test, as opposed to directional tests, is that the smooth character is largely maintained. We discuss both nested and non nested directional alternatives.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610921003637447