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 $\sup$ is finite there is always a best selection for a fixed number of cells. Equally likely cells are shown to be admissible when the alternative is large.
@article{1176343413,
author = {Spruill, M. C.},
title = {Cell Selection in the Chernoff-Lehmann Chi-Square Statistic},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 375-383},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343413}
}
Spruill, M. C. Cell Selection in the Chernoff-Lehmann Chi-Square Statistic. Ann. Statist., Tome 4 (1976) no. 1, pp. 375-383. http://gdmltest.u-ga.fr/item/1176343413/