On optimal asymptotic tests of composite hypotheses with several constraints

Summary A locally asymptotically most powerful test for composite hypotheses with t independent linear constraints on the parameters has been developed for the case where the observed random variables {X_nk, k=1,2,...,n} are independently but not necessarily identically distributed. However, their distributions depend on two vector parameters, one = (₁, ₂, ..., _t) being under test, and the other = (₁, ₂, ..., _s) being the nuisance parameter.This investigation was supported (in part) by a research grant (No. GM-10525(2)) from the National Institutes of Health, Public Health Service.On leave from UniversitÄt Heidelberg, Germany, and supported by a NATO research scholarship.