SPARSE TENSOR PRODUCT APPROXIMATION FOR A CLASS OF GENERALIZED METHOD OF MOMENTS ESTIMATORS

Generalized Method of Moments (GMM) estimators in their various forms, including the popular Maximum Likelihood (ML) estimator, are frequently applied for evaluation complex econometric models with not analytically computable moment or likelihood functions. As objective functions GMM- and ML-estimators themselves constitute approximation an integral, more precisely expected value over real world data space, question arises whether function simulation entire can be combined. Motivated by Probit Mixed Logit models, we consider double integrals a linking which stems from considered e.g. logarithm Likelihood, apply sparse tensor product quadrature to reduce computational effort combined integral. Given Holder continuity function, prove that this approach improve order convergence rate classical ML-estimator factor two, even integrands low regularity high dimensionality. This result is illustrated numerical simulations Multinomial estimated ML- GMM-estimators, respectively.