Optimal instrumental variable estimation and approximate implementations
Optimal instrumental variable estimation and approximate implementations
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DOI：
10.1109/tac.1983.1103312
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发表时间：
1983-07
影响因子：
6.8
通讯作者：
P. Stoica;T. Söderström
中科院分区：
文献类型：
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作者：
P. Stoica;T. Söderström
工具变量（IV）方法的精度特性进行了研究。分析中包括数据预过滤和使用其他工具等扩展。参数估计是渐近高斯分布。给出了它们分布的协方差矩阵的显式表达式。协方差矩阵然后被作为准确度的（多变量）测量。它示出了如何可以通过适当选择的仪器和预过滤器进行优化。这样得到的最佳工具变量估计不能直接使用，因为真实的系统和扰动的统计特性必须是已知的，以便计算最佳的仪器和预滤波器。一个多步骤的程序，包括三个或四个简单的步骤，然后提出了一种方法来克服这一困难。该过程包括使用诸如预测误差方法的统计有效方法将扰动建模为阿尔马过程。本文还分析了多步估计的统计性质。这些估计值也是渐近高斯分布的。将估计误差的协方差矩阵与对应于预测误差方法的协方差矩阵进行比较。对于某些模型结构，这两种方法给出了相同的渐近精度。结论是，多步过程，这是很容易实现，也有很好的唯一性，可以被看作是一个有趣的替代预测误差方法。
The accuracy properties of instrumental variables (IV) methods are investigated. Extensions such as prefiltering of data and use of additional instruments are included in the analysis. The parameter estimates are shown to be asymptotically Gaussian distributed. An explicit expression is given for the covariance matrix of their distribution. The covariance matrix is then taken as a (multivariable) measure of accuracy. It is shown how it can be optimized by an appropriate selection of instruments and prefilter. The so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters. A multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty. This procedure includes modeling of the disturbance as an ARMA process using a statistically efficient method such as a prediction error method. The statistical properties of the estimates obtained with the multistep procedure are also analyzed. Those estimates are shown to be asymptotically Gaussian distributed as well. The covariance matrix of the estimation errors is compared to that corresponding to a prediction error method. For some model structures these two approaches give the same asymptotic accuracy. The conclusion is that the multistep procedure, which is quite easy to implement and also has nice uniqueness properties, can be viewed as an interesting alternative to prediction error methods.