On the empirical likelihood ratio for smooth functions of M-functionals

It is known that the empirical likelihood ratio can be used to construct confidence regions for smooth functions of the mean, Fr\ue9chet differentiable statistical functionals and for a class of M-functionals. In this paper, we argue that this use can be extended to the class of functionals which are smooth functions of M-functionals. In particular, we find the conditions under which the empirical log-likelihood ratio for this kind of functionals admits a \u3c72 approxima tion. Furthermore, we investigate, by simulation methods, the related approximation error in some contexts of practical interest