Abstract
For a set of random variables, not necessarily independent, along with a characterization of locally most powerful (LMP) conditional tests, some weak as well as strong invariancc principles for tbe allied test statistics arc considered. In the light of asymptotic sufficiency of sub-sigma fields (generating tbe conditional tests). the closeness of LMP and LMP conditional test statistics is examined with reference to the invariancc principles for these statistics. these results include, as special cases, parallel results on various LMP rank test statistica. scattered in the literature.
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