Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have the same asymptotic efficiency properties as maximum likelihood under Gaussianity but are of closed form. Hence they are computationally simple and free from compactness assumptions, thereby avoiding two notorious pitfalls of implicitly defined estimates of large spatial autoregressions. When commencing from an initial least squares estimate, the Newton step can also lead to weaker regularity conditions for a central limit theorem than some extant in the literature. A simulation study demonstrates excellent finite sample gains from Newton iterations, especially in large multiparameter models for which grid search is costly. A small empirical illustration shows improvements in estimation precision with real data.

在参数空间作为样本大小函数缓慢增长的意义上，检查了具有大量参数的空间自回归模型的伪最大似然估计的牛顿步近似。它们具有与高斯性下的最大似然相同的渐近效率属性，但具有封闭形式。因此，它们在计算上很简单，并且不受紧凑性假设的影响，从而避免了隐式定义大空间自回归估计的两个臭名昭著的陷阱。当从初始最小二乘估计开始时，牛顿步骤还可能导致中心极限定理的正则性条件比文献中现存的一些更弱。模拟研究展示了牛顿迭代的出色有限样本增益，特别是在网格搜索成本高昂的大型多参数模型中。一个小的经验说明显示了真实数据的估计精度的提高。