A Limit Theorem for Some Modified Chi-Square Statistics when the Number of Classes Increases

F. C. Drost
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F. C. Drost: Free University, Dept. of Mathematics and Computer Science

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 43-58 from Springer

Abstract: 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.

Keywords: chi-square tests; location-scale parameter; goodness-of-fit; number of classes.; Primary 62E20; 62F20; secondary 62F05 (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-94-009-3965-3_5

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