空间自回归参数的调整后QMLE
Adjusted QMLE for the spatial autoregressive parameter
摘要：
减弱干扰参数对感兴趣的参数的最大似然估计的影响的一种简单且通常非常有效的方式是使该参数的简档分数重新居中。我们应用这个一般原则的准最大似然估计（QMLE）的自回归参数$λ$在空间自回归。与$λ$的QMLE相比，$λ$的估计量具有更好的有限样本性质，特别是在存在大量协变量的情况下。它还可以解决附带参数问题，例如，在具有网络固定效应的社会相互作用模型中，或在具有个体或时间固定效应的空间面板模型中。然而，空间自回归对这种类型的调整提出了特定的挑战，因为重新定位特征分数可能导致调整后的估计值超出$λ$的常用参数空间。这种情况发生的条件，并讨论了影响。对于推理，我们提出了置信区间的基础上的Lugannani-赖斯近似的分布调整后的QMLE的$λ$。根据我们的模拟，这些区间的覆盖特性是优秀的，即使在模型中有大量的协变量。
英文摘要：
One simple, and often very effective, way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter. We apply this general principle to the quasi-maximum likelihood estimator (QMLE) of the autoregressive parameter $λ$ in a spatial autoregression. The resulting estimator for $λ$ has better finite sample properties compared to the QMLE for $λ$, especially in the presence of a large number of covariates. It can also solve the incidental parameter problem that arises, for example, in social interaction models with network fixed effects, or in spatial panel models with individual or time fixed effects. However, spatial autoregressions present specific challenges for this type of adjustment, because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for $λ$. Conditions for this to happen are given, and implications are discussed. For inference, we propose confidence intervals based on a Lugannani--Rice approximation to the distribution of the adjusted QMLE of $λ$. Based on our simulations, the coverage properties of these intervals are excellent even in models with a large number of covariates.
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