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A locally asymptotically most powerful test for a composite hypothesis H: = ₀ has been developed for the case where the observable random variables \X₍₊, k = 1, 2, , n\ are independently but not necessarily identically distributed. However, their distributions depend on s + 1 parameters, one being under test and the other being a vector = (₁, , ₛ) of nuisance parameters. The theory is illustrated with an example from the field of astronomy.
Bartoo et al. (Fri,) studied this question.