Empirical likelihood for non-smooth criterion functions

Suppose that X1, ..., Xn is a sequence of independent random vectors, identically distributed as a d-dimensional random vector X. Let µ ∈ IR p be a parameter of interest and ν ∈ IR q be some nuisance parameter. The unknown, true parameters (µ0 , ν0 ) are uniquely determined by the system of equations E {g(X, µ0 , ν0 )} = 0, where g = (g1, ..., gp+q ) is a vector of p + q functions. In this paper we develop an empirical likelihood method to do inference for the parameter µ0. The results in this paper are valid under very mild conditions on the vector of criterion functions g. In particular, we do not require that g1,..., gp+q are smooth in µ or ν. This offers the advantage that the criterion function may involve indicators, which are encountered when considering e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed empirical likelihood method for small samples.

• metadata
• relations

Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2008
Language	Anglais
Number of pages	25 pages
Collection	STAT Discussion Paper - 0812
Affiliations	Universidad Carlos III - Departamento de Estadística UCL - EUEN/STAT - Institut de statistique Universiteit Hasselt - Center for statistics
Keywords	copulas ; empirical likelihood ; estimating equations ; hypothesis testing ; nuisance parameter ; quantiles ; ROC curve ; Confidence region
Links	http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html#2008 http://hdl.handle.net/2078.1/116114[Handle]

See also
	[boreal:35376]	Empirical Likelihood for Non-Smooth Criterion Functions