AISM 54, 585-594
© 2002 ISM
(Received July 17, 2000; revised February 5, 2001)
Abstract. Let $f_0(x)$ be the exponential density and $f_\gamma(x)$ 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.
Key words and phrases: Mixture models, likelihood test, exponential distribution.