A generalized method of moments (GMM) estimator is unreliable for a large number of moment conditions, that is, it is comparable, or larger than the sample size. While classical GMM literature proposes several provisions to this problem, its Bayesian counterpart (i.e., Bayesian inference using a GMM criterion as a quasi-likelihood) almost totally ignores it. This study bridges this gap by proposing an adaptive Markov Chain Monte Carlo (MCMC) approach to a GMM inference with many moment conditions. Particularly, this study focuses on the adaptive tuning of a weighting matrix on the fly. Our proposal consists of two elements. The first is the use of the nonparametric eigenvalue-regularized precision matrix estimator, which contributes to numerical stability. The second is the random update of a weighting matrix, which substantially reduces computational cost, while maintaining the accuracy of the estimation. We then present a simulation study and real data application to compare the performance of the proposed approach with existing approaches.
翻译：一种通用的瞬间估计方法(GMM)对于许多时刻条件来说是不可靠的,也就是说,它可以比较,或者比样本大小大。传统的GMM文献对这一问题提出了若干规定,但古典的GMM文献对此问题提出了若干规定,而其巴伊西亚对应的文献(即使用GMM标准作为准类似标准的Bayesian推论)几乎完全忽略了这一规定。本研究报告建议对GMM的推理采用适应性的Markov 链 Monte Carlo(MCMC) 方法,从而弥补这一差距,同时提出一个适应性的Markov 链 Monte Carlo(MC) 方法,与许多时刻的推理。特别是,本研究报告侧重于对飞翔的加权矩阵的调整。我们的提议包括两个要素。第一个是使用非对等的半数值值定序精确矩阵估测算器,有助于数字稳定性。第二个是随机更新一个加权矩阵,该矩阵大大降低了计算成本,同时保持估算的准确性。我们随后提出模拟研究和实际数据应用,以便比较拟议方法与现有方法的性。
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