Statistical spatial series modelling II: Some further results on unilateral lattice processes
Statistical spatial series modelling II: Some further results on unilateral lattice processes
复制标题
统计空间序列建模II：单边晶格过程的一些进一步结果
DOI：
10.2307/1426619
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发表时间：
1983
影响因子：
1.2
通讯作者：
D. Tjøstheim
中科院分区：
文献类型：
--
作者：
D. Tjøstheim
本文给出了空间序列类F（x1，· ··，xn）的估计的一个渐近理论，其中（x1，· ··，xn）在正则格上变化.研究了两类单边模型，即半空间模型和因果（象限型）模型。结果表明，一些渐近结果是共同的，这些模型。对实际应用特别感兴趣的是确定应该包括多少参数来描述每个方向上的依赖程度的问题。在这里，我们能够获得弱一致的推广熟悉的时间序列标准的假设下，模型的生成变量是独立和同分布的。对于因果模型，我们引入了空间创新过程和格鞅的概念，并使用这些扩展的渐近理论的情况下，某种类型的依赖是允许的生成变量。
An asymptotic theory of estimation is developed for classes of spatial series F(x 1, · ··, xn ), where (x 1, · ··, xn ) varies over a regular cartesian lattice. Two classes of unilateral models are studied, namely half-space models and causal (quadrant-type) models. It is shown that a number of asymptotic results are common for these models. Of special interest for practical applications is the problem of determining how many parameters should be included to describe the degree of dependence in each direction. Here we are able to obtain weakly consistent generalizations of familiar time-series criteria under the assumption that the generating variables of the model are independently and identically distributed. For causal models we introduce the concepts of spatial innovation process and lattice martingale and use these to extend some of the asymptotic theory to the case where a certain type of dependence is permitted in the generating variables.