空间自回归模型的组合矩方程方法

Pub Date : 2023-07-08 DOI:10.1002/cjs.11784
Jiaxin Liu, Hongliang Liu, Yi Li, Huazhen Lin
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引用次数: 0

摘要

现有的空间自回归模型拟合方法各有优缺点。例如,最大似然估计法(MLE)可以得到有效的估计值,但计算负担较重。计算效率高的方法,如广义矩法(GMMs)和空间两阶段最小二乘法(2SLS),通常要求外生协变量显著,这一限制性假设在实践中可能会失效。我们提出了一种新的估计方程方法,称为组合矩方程(COME),它将第一矩与残差项的协方差条件相结合。与 MLE 相比,所提出的估计方法对计算的要求更低,而且不需要 GMM 和 2SLS 所要求的限制性外生条件。我们证明了所提出的估计方法是一致的,并建立了其渐近分布。大量的模拟证明,所提出的方法在偏差、效率和计算方面都优于竞争对手。我们将提出的方法用于分析一项空气污染研究,并获得了有关北京 PM2.5 浓度空间分布的一些有趣结果。
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A combined moment equation approach for spatial autoregressive models

Existing methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two-stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing.

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