We apply the results of the above talk 
to the asymptotic study of mixture of Gaussian 
distributions or particular translation distributions. In particular we consider the power 
of the likelihood ratio test under contiguous hypotheses.

It is shown that for arbitrary large domain of the parameters of the mixture, the 
test is worthless : the power is arbitrary close to the level.  


Joint work with Jean-Marc Azai s and Elisabeth Gassiat