Local Score Tests in Mixture Exponential Family with Fixed Mean

Abstract

Abstract In this paper, the testing problem for homogeneity is considered in the mixture exponential density or probability distribution family {f(x|θ1, θ2, λ,) = (1 - λ)fθ1(x) + λfθ2(x)} where {fθ(x) = f0(x)exp(xθ - c(θ))} belongs to a standard one-parameter exponential family for |θ| ≤ K (>0). Assuming the mean is fixed and unknown, a local score-based test is proposed which naturally generalizes Neyman and Scott's C(α)-test. Simulation results show that the proposed test improves C(α)-test in certain cases. The test does not involve the boundedness problem of the mean parameter space and the results continue the work of Wu and Gupta (2003).