Abstract
In this paper, we introduce a robust version of the empirical likelihood estimator for semiparametric moment condition models. This estimator is obtained by minimizing the modified Kullback–Leibler divergence, in its dual form, using truncated orthogonality functions. We prove the robustness and the consistency of the new estimator. The performance of the robust empirical likelihood estimator is illustrated through examples based on Monte Carlo simulations.
Highlights
A moment condition model is a family M(1) of probability measures (p.m.), all defined on the same measurable space (Rm, B(Rm )), such that (s.t.)Citation: Keziou, A.; Toma, A
The reference model will be associated with the truncated orthogonality function that will be used to define the robust version of the Empirical Likelihood (EL) estimator of the parameter θ0
It holds that the equation R g( x, θ ) dP0 ( x ) = 0, with g( x, θ ) = ( x − θ, x2 − θ 2 − 2θ )>, has a unique solution θ = θ0 = 1. This is a particular case of the model from Example 1, namely when h(θ ) = θ 2 + θ
Summary
Department of Applied Mathematics, Bucharest University of Economic Studies, Piaţa Romană no. 6, 010374 Bucharest, Romania “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie no. 13, 050711 Bucharest, Romania These authors contributed equally to this work.
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