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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9856

Title: Empirical Likelihood for Non-Smooth Criterion Functions
Authors: MOLANES LOPEZ, Elisa Maria
VAN KEILEGOM, Ingrid
VERAVERBEKE, Noel
Issue Date: 2009
Publisher: WILEY-BLACKWELL PUBLISHING, INC
Citation: SCANDINAVIAN JOURNAL OF STATISTICS, 36(3). p. 413-432
Abstract: Suppose that X-1,..., X-n is a sequence of independent random vectors, identically distributed as a d-dimensional random vector X. Let mu is an element of R-p be a parameter of interest and nu is an element of R-q be some nuisance parameter. The unknown, true parameters (mu(0), nu(0)) are uniquely determined by the system of equations E{g(X, mu(0), nu(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 mu(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 mu or nu. 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.
Notes: [Van Keilegom, Ingrid] Univ Catholique Louvain, Inst Stat, B-1348 Louvain, Belgium. [Molanes Lopez, Elisa M.] Univ Carlos III Madrid, Dept Estadist, E-28903 Getafe, Spain. [Veraverbeke, Noel] Univ Hasselt, Ctr Stat, Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/9856
DOI: 10.1111/j.1467-9469.2009.00640.x
ISI #: 000268988600003
ISSN: 0303-6898
Category: A1
Type: Journal Contribution
Validation: ecoom, 2010
Appears in Collections: Research publications

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