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B0825
Title: Efficient and simple testing procedures for the (extended) generalized inverse Gaussian models Authors:  Efoevi Angelo Koudou - IECL CNRS /Universite de Lorraine (France) [presenting]
Christophe Ley - University of Luxembourg (Luxembourg)
Abstract: The standard efficient testing procedures in the Generalized Inverse Gaussian (GIG) family are likelihood ratio tests, hence rely on Maximum Likelihood (ML) estimation of the three parameters of the GIG. The particular form of GIG densities, involving modified Bessel functions, prevents in general from a closed-form expression for ML estimators, which are obtained at the expense of complex numerical approximation methods. On the contrary, Method of Moments (MM) estimators allow for concise expressions, but tests based on these estimators suffer from a lack of efficiency compared to likelihood ratio tests. This is why, in recent years, trade-offs between ML and MM estimators have been proposed, resulting in simpler yet not completely efficient estimators and tests. The presented method does not propose such a trade-off but rather an optimal combination of both methods. The proposed tests inherit efficiency from an ML-like construction and simplicity from the MM estimators of the nuisance parameters. They rely on the Le Cam methodology. Besides providing simple efficient testing methods, the theoretical background of this methodology further allows to write out explicitly power expressions for the proposed tests. A Monte Carlo simulation study shows that, also at small sample sizes, these simpler procedures do at least as good as the complex likelihood ratio tests. Steps towards an application of the same method to the Extended GIG models will be discussed.