Abstract
It is well known that likelihood ratio statistic is Bartlett correctable. We consider decomposition of a likelihood ratio statistic into 1 degree of freedom components based on sequence of nested hypotheses. We give a proof of the fact that the component likelihood ratio statistics are distributed mutually independently up to the order O(1/n) and each component is independently Bartlett correctable. This was implicit in Lawley (1956, Biometrika, 43, 295–303) and proved in Bickel and Ghosh (1990, Ann. Statist., 18, 1070–1090) using a Bayes method. We present a more direct frequentist proof.
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Takemura, A., Kuriki, S. A proof of independent Bartlett correctability of nested likelihood ratio tests. Ann Inst Stat Math 48, 603–620 (1996). https://doi.org/10.1007/BF00052322
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DOI: https://doi.org/10.1007/BF00052322