Reweighted Smooth Tests of Goodness of Fit

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 9; pp. 1651 - 1670
• Main Authors: De Boeck, B., Thas, O., Ottoy, J. P.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01-01-2011; Taylor & Francis; Taylor & Francis Ltd
• 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; Polynomial; Score test; 62-02; Statistical distribution; Weighted test; Goodness of fit test; Directional alternative; Statistical method; 62E20; Smooth test; Hilbert space; Approximation theory; Test power; Orthonormal polynomials; 62F03; Power
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610921003637447

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.