Maximum likelihood estimation of the model parameters for a spatial population based on data collected from a survey sample is usually straightforward when sampling and non-response are both non-informative, since the model can then usually be fitted using the available sample data, and no allowance is necessary for the fact that only a part of the population has been observed. Although for many regression models this naive strategy yields consistent estimates, this is not the case for some models, such as spatial auto-regressive models. In this paper, we show that for a broad class of such models, a maximum marginal likelihood approach that uses both sample and population data leads to more efficient estimates since it uses spatial information from sampled as well as non-sampled units. Extensive simulation experiments based on two well-known data sets are used to assess the impact of the spatial sampling design, the auto-correlation parameter and the sample size on the performance of this approach. When compared to some widely used methods that use only sample data, the results from these experiments show that the maximum marginal likelihood approach is much more precise.

中文翻译：

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基于样本调查数据的空间自相关和自回归模型估计

当抽样和无响应都没有信息时，基于从调查样本收集的数据对空间总体的模型参数进行最大似然估计通常很简单，因为通常可以使用可用的样本数据拟合模型，而没有由于仅观察了一部分人口这一事实，因此需要考虑。尽管对于许多回归模型，这种朴素的策略会产生一致的估计，但对于某些模型（例如空间自回归模型）而言，情况并非如此。在本文中，我们展示了对于一大类此类模型，使用样本和总体数据的最大边际似然方法会导致更有效的估计，因为它使用来自抽样和非抽样单位的空间信息。基于两个众所周知的数据集的大量模拟实验用于评估空间采样设计、自相关参数和样本大小对这种方法性能的影响。与一些广泛使用的仅使用样本数据的方法相比，这些实验的结果表明，最大边际似然方法要精确得多。