It is known that the empirical likelihood ratio can be used to construct confidence regions for smooth functions of the mean, Fréchet 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 χ2 approxima tion. Furthermore, we investigate, by simulation methods, the related approximation error in some contexts of practical interest.
On the empirical likelihood ratio for smooth functions of M-functionals
ADIMARI, GIANFRANCO
1997
Abstract
It is known that the empirical likelihood ratio can be used to construct confidence regions for smooth functions of the mean, Fréchet 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 χ2 approxima tion. Furthermore, we investigate, by simulation methods, the related approximation error in some contexts of practical interest.
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