Abstract
Let f 0(x) be the exponential density and f γ(x) the translation model. Let (X i) i=1,n be i.i.d. random variables, with density g. We test that g is f 0 against g is a simple mixture, using the LRT statistic. We prove that the LRT diverges to infinity with probability 1/2 and it is equal to 0 with probability 1/2. Therefore, the classical likelihood limiting theory does not hold.
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Ciuperca, G. Likelihood Ratio Statistic for Exponential Mixtures. Annals of the Institute of Statistical Mathematics 54, 585–594 (2002). https://doi.org/10.1023/A:1022415228062
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DOI: https://doi.org/10.1023/A:1022415228062