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  4. Sparse Tensor Product Approximation for a Class of Generalized Method of Moments Estimators
 
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2022
Journal Article
Titel

Sparse Tensor Product Approximation for a Class of Generalized Method of Moments Estimators

Abstract
Generalized method of moments (GMM) estimators in their various forms, including the popular maximum likelihood (ML) estimator, are frequently applied for the evaluation of complex econometric models without analytically computable moment or likelihood functions. As the objective functions of GMM-and ML-estimators themselves constitute the approximation of an integral, more precisely of the expected value over the real world data space, the question arises whether the approximation of the moment function and the simulation of the entire objective function can be combined. Motivated by the popular probit and mixed logit models, we consider double integrals with a linking function that stems from the considered estimator (e.g., the logarithm for ML) and apply a sparse tensor product quadrature to reduce the computational effort for the approximation of the combined integral. Given Hölder continuity of the linking function, we prove that this approach can improve the order of the convergence rate of the classical GMM-and ML-estimator by a factor of two, even for integrands of low regularity or high dimensionality. This result is il-lustrated by numerical simulations of mixed logit and multinomial probit integrals, which are estimated by ML-and GMM-estimators, respectively.
Author(s)
Gilch, A.
Institute for Numerical Simulation
Griebel, Michael
Institute for Numerical Simulation
Oettershagen, J.
Institute for Numerical Simulation
Zeitschrift
International journal for uncertainty quantification
Thumbnail Image
DOI
10.1615/Int.J.UncertaintyQuantification.2021037549
Language
English
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Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Tags
  • discrete choice model...

  • generalized method of...

  • maximum likelihood

  • maximum simulated lik...

  • multilevel estimation...

  • numerical integration...

  • optimal weights cubat...

  • sparse grids

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