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首页> 外文期刊>IEEE Transactions on Signal Processing >Bounded Influence Propagation τ -Estimation: A New Robust Method for ARMA Model Estimation
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Bounded Influence Propagation τ -Estimation: A New Robust Method for ARMA Model Estimation

机译：有限影响传播τ-估计：ARMA模型估计的一种新的鲁棒方法

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摘要

A new robust and statistically efficient estimator for ARMA models called the bounded influence propagation τ-estimator is proposed. The estimator incorporates an auxiliary model, which prevents the propagation of outliers. Strong consistency and asymptotic normality of the estimator for ARMA models that are driven by independently and identically distributed (iid) innovations with symmetric distributions are established. To analyze the infinitesimal effect of outliers on the estimator, the influence function is derived and computed explicitly for an AR(1) model with additive outliers. To obtain estimates for the AR(p) model, a robust Durbin–Levinson type and a forward–backward algorithm are proposed. An iterative algorithm to robustly obtain ARMA(p,q) parameter estimates is also presented. The problem of finding a robust initialization is addressed, which for orders p+q>2 is a nontrivial matter. Numerical experiments are conducted to compare the finite sample performance of the proposed estimator to existing robust methodologies for different types of outliers both in terms of average and of worst case performance, as measured by the maximum bias curve. To illustrate the practical applicability of the proposed estimator, a real-data example of outlier cleaning for R–R interval plots derived from electrocardiographic data is considered. The proposed estimator is not limited to biomedical applications, but is also useful in any real-world problem whose observations can be modeled as an ARMA process disturbed by outliers or impulsive noise.
机译：提出了一种新的鲁棒且统计有效的ARMA模型估计器，称为有界影响传播τ估计器。估计器包含一个辅助模型，可防止异常值的传播。建立了ARMA模型的估计器的强一致性和渐近正态性，该模型由具有对称分布的独立且相同分布（iid）创新驱动。为了分析离群值对估计量的无穷小影响，导出影响函数并明确计算具有加和离群值的AR（1）模型的影响函数。为了获得AR（p）模型的估计，提出了鲁棒的Durbin-Levinson类型和前向后向算法。还提出了一种鲁棒性获得ARMA（p，q）参数估计的迭代算法。解决了寻找健壮的初始化的问题，对于阶数p + q> 2而言，这是不平凡的事情。进行了数值实验，将建议的估计量的有限样本性能与现有的针对不同类型离群值的鲁棒方法相比，无论是平均性能还是最坏情况的性能，均以最大偏差曲线衡量。为了说明所提出的估算器的实际适用性，我们考虑了从心电图数据得出的R–R间隔图的离群值清理的真实数据示例。所提出的估计器不仅限于生物医学应用，还可以用于任何现实世界中的问题，这些问题的观察结果可以建模为离群值或脉冲噪声干扰的ARMA过程。

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