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- Title
Empirical Likelihood for Non-Smooth Criterion Functions.
- Authors
LOPEZ, ELISA M. MOLANES; VAN KEILEGOM, INGRID; VERAVERBEKE, NOËL
- Abstract
Suppose that X 1,..., X n is a sequence of independent random vectors, identically distributed as a d-dimensional random vector X. Let be a parameter of interest and be some nuisance parameter. The unknown, true parameters ( μ 0, ν 0) are uniquely determined by the system of equations E{ g( X, μ 0, ν 0)} = 0, where g = ( g 1,..., g p+ q) is a vector of p+ q functions. In this paper we develop an empirical likelihood (EL) method to do inference for the parameter μ 0. 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 g 1,..., g p+ 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 EL method for small samples.
- Subjects
STATISTICS; EQUATIONS; REGRESSION analysis; HYPOTHESIS; MATHEMATICS
- Publication
Scandinavian Journal of Statistics, 2009, Vol 36, Issue 3, p413
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2009.00640.x