Abstract
In this paper, the testing problem for homogeneity is considered in the mixture exponential density or probability distribution family \(\{f(x\mid\theta_1,\theta_2,\lambda)=(1-\lambda)f_{\theta_1}(x)+\lambda f_{\theta_2}(x)\}\) where {f θ (x) = f 0(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).
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Gupta, A.K., Wu, Y. Local Score Tests in Mixture Exponential Family with Fixed Mean. J Stat Theory Pract 4, 757–771 (2010). https://doi.org/10.1080/15598608.2010.10412017
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DOI: https://doi.org/10.1080/15598608.2010.10412017