Abstract
In the presence of a location-scale nuisance parameter we consider three chi-square type tests based on increasingly finer partitions as the sample size increases. The asymptotic distributions are derived both under the null-hypothesis and under local alternatives, obtained by taking contamination families of densities between the null-hypothesis and fixed alternative hypotheses. As a consequence of our main theorem it is shown that the Rao-Robson-Nikulin test asymptotically dominates the Watson-Roy test and the Dzhaparidze-Nikulin test. Conditions are given when it is optimal to let the number of classes increase to infinity.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Drost, F.C. (1987). A Limit Theorem for Some Modified Chi-Square Statistics when the Number of Classes Increases. In: Bauer, P., Konecny, F., Wertz, W. (eds) Mathematical Statistics and Probability Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3965-3_5
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DOI: https://doi.org/10.1007/978-94-009-3965-3_5
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