Likelihood Ratio Statistic for Exponential Mixtures
- Cite this article as:
- Ciuperca, G. Annals of the Institute of Statistical Mathematics (2002) 54: 585. doi:10.1023/A:1022415228062
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Let f0(x) be the exponential density and fγ(x) the translation model. Let (Xi)i=1,n be i.i.d. random variables, with density g. We test that g is f0 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.