Do components of smooth tests of fit have diagnostic properties? |
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Authors: | Norbert Henze |
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Institution: | 1. Institut für Mathematische Stochastik, Universit?t Karlsruhe, Englerstr. 2, 76128, Karlsruhe, Germany
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Abstract: | Smooth goodness of fit tests were introduced by Neyman (1937). They can be regarded as a compromise between globally consistent
(“omnibus”) tests of fit and procedures having high power in the direction of a specific alternative. It is commonly believed
that components of smooth tests like, e.g., skewness and kurtosis measures in the context of testing for normality, have special
diagnostic properties in case of rejection of a hypothesisH
0 in the sense that they constitute direct measures of the kind of departure fromH
0. Recent years, however, have witnessed a complete change of attitude towards the diagnostic capabilities of skewness and
kurtosis measures in connection with normality testing. In this paper, we argue that any component of any smooth test of fit
is strictly non-diagnostic when used conventionally. However, a proper rescaling of components does indeed achieve the desired
“directed diagnosis”. |
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Keywords: | Goodness of fit smooth tests components directed diagnosis |
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