Geodesic
Modified power divergence estimators in normal models – simulation and comparative study
Kybernetika, Tome 48 (2012) no. 4, pp. 795-808.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{KYB_2012__48_4_a8,
     author = {Fr\'ydlov\'a, Iva and Vajda, Igor and K\r{u}s, V\'aclav},
     title = {Modified power divergence estimators in normal models {\textendash} simulation and comparative study},
     journal = {Kybernetika},
     pages = {795--808},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2012},
     mrnumber = {3013399},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a8/}
}
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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/