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Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms

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  • Maria P. Braun
  • Simos G. Meintanis
  • Viatcheslav B. Melas

Abstract

Parameter estimation based on the generalized method of moments (GMM) is proposed. The proposed method employs a distance between an empirical and the corresponding theoretical transform. Estimation by the empirical characteristic function (CF) is a typical example, but alternative empirical transforms are also employed, such as the empirical Laplace transform when dealing with non‐negative random variables. D‐optimal designs are discussed, whereby the arguments of the empirical transform are chosen by maximizing the determinant of the asymptotic Fisher information matrix for the resulting estimators. The methods are applied to some parametric models for which classical inference is complicated. Nous proposons une technique d'estimation paramétrique fondée sur la méthode généralisée des moments. Cette méthode utilise une distance entre la transformée empirique et la transformée théorique correspondantes. L'estimation à l'aide de la fonction caractéristique empirique est un exemple typique, mais d'autres transformées empiriques sont également employées, telle que la transformée de Laplace empirique, lorsqu'il s'agit de variables aléatoires positives. Des plans d'expérience D‐optimaux sont examinés, où les arguments de la transformée empirique sont choisis en maximisant le déterminant de la matrice d'information asymptotique de Fisher pour les estimateurs obtenus. Ces méthodes sont appliquées à certains modèles paramétriques pour lesquels les techniques d'inférence classiques sont compliquées. Mots‐clés: Fonction caractéristique empirique, Transformée de Laplace empirique, Estimation paramétrique, Modèle de Gaussienne inverse normale, Modèle de variance Gamma normale.

Suggested Citation

  • Maria P. Braun & Simos G. Meintanis & Viatcheslav B. Melas, 2008. "Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms," International Statistical Review, International Statistical Institute, vol. 76(3), pages 387-400, December.
  • Handle: RePEc:bla:istatr:v:76:y:2008:i:3:p:387-400
    DOI: 10.1111/j.1751-5823.2008.00055.x
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    References listed on IDEAS

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    2. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.

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