Abstract

We consider the problem of estimating the parameters of an autoregressive process based on observations with additive noise. A sequential method has been developed for constructing a fixed-size confidence domain with a given confidence factor for a vector of unknown parameters based on a finite sample. Formulas are obtained for the duration of a procedure that achieves the required performance of estimates of unknown parameters in the case of Gaussian noise. Confidence parameter estimates are constructed using a special sequential modification of the classic Yule–Walker estimates; this permits one to estimate the confidence factor for small and moderate sample sizes. The results of numerical modeling of the proposed estimates are presented and compared with the Yule–Walker estimates using the example of confidence estimation of spectral density.

中文翻译：

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基于噪声数据的自回归参数的置信度估计

摘要

我们考虑基于加性噪声的观察来估计自回归过程的参数的问题。已经开发了一种顺序方法，用于基于有限样本为未知参数的向量构造具有给定置信因子的固定大小置信域。在高斯噪声的情况下实现未知参数估计所需性能的程序持续时间获得公式。置信参数估计是使用经典 Yule-Walker 估计的特殊顺序修改构建的；这允许人们估计小样本和中等样本大小的置信因子。使用谱密度置信度估计的例子，提出了建议估计的数值建模结果，并与 Yule-Walker 估计进行了比较。