On Optimal Asymptotic Tests of Composite Statistical Hypotheses

A locally asymptotically most powerful test for a composite hypothesis H:ξ = ξ₀ has been developed for the case where the observable random variables ₙₖ, k = 1, 2, ⋯, n\ are independently but not necessarily identically distributed. However, their distributions depend on $s + 1$ parameters, one being ξ under test and the other being a vector θ = (θ₁, ⋯, θₛ) of nuisance parameters. The theory is illustrated with an example from the field of astronomy.