论文标题
一类通用量估计器的广义方法的稀疏张量产品近似
Sparse tensor product approximation for a class of generalized method of moments estimators
论文作者
论文摘要
各种形式的矩（GMM）估计量（包括流行的最大可能性（ML）估计量）的广义方法经常用于评估具有不可分析计算的时刻或可能性函数的复杂计量经济学模型。由于GMM和ML估计器的目标函数本身构成了积分不可或缺的近似，更准确地说是对现实世界数据空间的期望值的近似，因此问题是否可以组合到矩函数的近似以及整个目标函数的模拟。由流行的概率和混合logit模型的动机，我们考虑具有链接函数的双重积分，该函数源于考虑的估计器，例如最大可能性的对数，并应用稀疏的张量产品正交，以减少组合积分的近似值的计算工作。鉴于链接函数的Hölder连续性，我们证明这种方法可以提高经典GMM和ML估计器的收敛速率的顺序，即使对于低规律性或较高维度的整数也是如此。该结果通过混合logit和多项式概率积分的数值模拟进行了说明，这些模拟分别由ML-和GMM估计器估算。
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 with not 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 which stems from the considered estimator, e.g. the logarithm for Maximum Likelihood, 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 illustrated by numerical simulations of Mixed Logit and Multinomial Probit integrals which are estimated by ML- and GMM-estimators, respectively.
