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Cell Selection in the Chernoff-Lehmann Chi-Square Statistic
The approximate Bahadur slope of the Chernoff-Lehmann $\chi^2$-test-of-fit to a scale-location family on $R^k$ is computed. The goal is to select cells (whose number is independent of sample size) to maximize this slope. The supremum is found and is shown to be a maximum only in trivial cases. If the …