A proof of independent Bartlett correctability of nested likelihood ratio tests
نویسندگان
چکیده
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 rst shown in Bickel and Ghosh (1990) using a Bayes method. We present a more direct frequentist proof.
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