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Modified power divergence estimators in normal models – simulation and comparative study
Kybernetika, Tome 48 (2012) no. 4, pp. 795-808 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Point estimators based on minimization of information-theoretic divergences between empirical and hypothetical distribution induce a problem when working with continuous families which are measure-theoretically orthogonal with the family of empirical distributions. In this case, the $\phi$-divergence is always equal to its upper bound, and the minimum $\phi$-divergence estimates are trivial. Broniatowski and Vajda [3] proposed several modifications of the minimum divergence rule to provide a solution to the above mentioned problem. We examine these new estimation methods with respect to consistency, robustness and efficiency through an extended simulation study. We focus on the well-known family of power divergences parametrized by $\alpha \in \mathbb{R}$ in the Gaussian model, and we perform a comparative computer simulation for several randomly selected contaminated and uncontaminated data sets, different sample sizes and different $\phi$-divergence parameters.
Point estimators based on minimization of information-theoretic divergences between empirical and hypothetical distribution induce a problem when working with continuous families which are measure-theoretically orthogonal with the family of empirical distributions. In this case, the $\phi$-divergence is always equal to its upper bound, and the minimum $\phi$-divergence estimates are trivial. Broniatowski and Vajda [3] proposed several modifications of the minimum divergence rule to provide a solution to the above mentioned problem. We examine these new estimation methods with respect to consistency, robustness and efficiency through an extended simulation study. We focus on the well-known family of power divergences parametrized by $\alpha \in \mathbb{R}$ in the Gaussian model, and we perform a comparative computer simulation for several randomly selected contaminated and uncontaminated data sets, different sample sizes and different $\phi$-divergence parameters.
Classification : 62B05, 62H30
Keywords: minimum $\phi $-divergence estimation; subdivergence; superdivergence; PC simulation; relative efficiency; robustness 
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Frýdlová, Iva; Vajda, Igor; Kůs, Václav. Modified power divergence estimators in normal models – simulation and comparative study. Kybernetika, Tome 48 (2012) no. 4, pp. 795-808. http://geodesic.mathdoc.fr/item/KYB_2012_48_4_a8/

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