The statistical theory of linear systems
The statistical theory of linear systems
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DOI：
10.2307/2983139
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发表时间：
1989-05
期刊：
影响因子：
--
通讯作者：
H. Tong;E. Hannan;M. Deistler
中科院分区：
文献类型：
--
作者：
H. Tong;E. Hannan;M. Deistler
本章讨论了ARMAX模型的一个相当完整的推理理论的发展。开发中的第一个问题是这种结构的空间协调。坐标是计算所必需的，因为中心极限定理必须用坐标来表示。一种这样的坐标化将遵循在标量m.f.d.中使用g、h、j中的系数矩阵，但还有很多其他的。本章重点介绍了ARMAX系统的代数和拓扑描述。在这方面，控制工程师起了主要作用。本章重点介绍最大似然（ML）估计量的渐近性质。通过优化这种可能性获得ML估计量。本章解释了这些估计量的渐近性质，而不假设数据是高斯分布的，并讨论了似乎是最小的假设的基础。
Publisher Summary The chapter discusses the development of a rather complete inferential theory for ARMAX models. The first problem in the development is the coordinatization of spaces of such structures. Coordinates are needed both for computations and because a central limit theorem must be expressed in terms of them. One such coordinatization would follow from the use of the coefficient matrices in g, h, j in the scalar m.f.d., but there are many others. The chapter highlights the algebraic and topological description of ARMAX systems. In this connection, control engineers have played a premier part. The chapter focuses on the asymptotic properties of maximum likelihood (ML) estimators. The ML estimator is obtained by optimizing this likelihood. The chapter explains the asymptotic properties of these estimators without assuming the data to be Gaussian and also discusses the basis of the assumptions that appear to be minimal.