动态估计中基于最小绝对偏差法的数据回归分析

A. A. Golovanov, A. Tyrsin
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引用次数: 0

摘要

在动态系统估计问题中应用回归分析需要一种高速的模型参数确定算法。此外,原始数据可能具有随机异质性,这就要求模型参数的估计必须能够抵抗各种数据异常。然而,稳定估计方法,包括最小绝对偏差法,明显不如参数估计方法。本研究的目的是描述一种计算效率高的算法,以实现最小绝对偏差法对回归模型的动态估计,并研究其解决实际问题的能力。该算法基于沿节点线下降。在这种情况下,考虑的不是目标函数的值,而是它在下降方向上的导数。由于使用前一步问题的解作为起点,并有效地更新当前数据样本中的观测值,因此降低了算法的计算复杂度。将本文提出的节点线梯度下降算法的动态版本与静态版本和最小二乘法的外部性能进行了比较。结果表明,基于节点线的梯度下降算法的动态版本可以使其在一般实际情况下的速度接近最小二乘法的速度,并可用于广泛类型系统的动态估计问题。
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Regression analysis of data based on the method of least absolute deviations in dynamic estimation problems
The use of regression analysis in dynamic problems of system estimation requires a high-speed algorithm of model parameter determination. Moreover, the original data may have stochastic heterogeneity which entails the necessity of the estimates of model parameters be resistant to various data anomalies. However, stable estimation methods, including the least absolute deviations method, are significantly inferior to the parametric ones. The goal of the study is to describe a computationally efficient algorithm for implementing the method of least absolute deviations for dynamic estimation of regression models and to study its capabilities for solving practical problems. This algorithm is based on descending along nodal lines. In this case, instead of the values of the objective function, its derivative in the direction of descent is considered. The computational complexity of the algorithm is also reduced due to the use of the solution of the problem at the previous step as a starting point and efficient updating of observations in the current data sample. The external performance of the proposed dynamic version of the algorithm of gradient descent along nodal lines has been compared with the static version and with the least squares method. It is shown that the dynamic version of the algorithm of gradient descent along the nodal lines make it possible to bring the speed close to that of the least squares method for common practical situations and to use the proposed version in dynamic estimation problems for a wide class of systems.
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