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Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms
Author(s) -
Braun Maria P.,
Meintanis Simos G.,
Melas Viatcheslav B.
Publication year - 2008
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2008.00055.x
Subject(s) - estimator , mathematics , empirical likelihood , laplace transform , parametric statistics , inference , generalized method of moments , function (biology) , mathematical optimization , statistics , computer science , artificial intelligence , mathematical analysis , evolutionary biology , biology
Summary 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.