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Mis-specification analysis of Wiener degradation models by using f- divergence with outliers

机译：使用离群值的f-散度对Wiener退化模型进行误判分析

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摘要

Degradation models have been investigated extensively for the evaluation of the quality and reliability of highly reliable products. In practical applications, the proper model of a degradation dataset is often unknown and misspecified for one thing; the dataset may be contaminated or contains outliers for another. Here, contamination means the degradation measurements are inspected embedded by noise with different levels. Thus, it is necessary to discuss the model mis-specification analysis and degradation data analysis when the degradation measurements contain outliers. Information geometry is a theory of using modern differential geometry to investigate the structure of manifolds induced by the statistical models, and the f-divergence is a popular tool in information geometry. This paper focuses on the model mis-specification analysis by employing the f-divergence as a tool to measure the difference between the true model and suggested models. A robust parameter estimation method based on minimizing the f-divergence is proposed. The results based on Kullback Leibler divergence are obtained as an illustration. Simulation results and two numerical examples are used to illustrate the advantages of the proposed methodologies.
机译：退化模型已被广泛研究，以评估高度可靠产品的质量和可靠性。在实际应用中，降级数据集的正确模型通常是未知的，并且由于一件事而错误指定。该数据集可能被污染或包含另一个的离群值。在这里，污染是指通过不同级别的噪声来检查退化测量结果。因此，当退化测量值包含异常值时，有必要讨论模型的错误规格分析和退化数据分析。信息几何学是一种利用现代微分几何学研究统计模型诱导的流形结构的理论，而f散度是信息几何学中的一种流行工具。本文通过使用f散度作为工具来度量模型错误规格分析，以衡量真实模型与建议模型之间的差异。提出了一种基于最小化f散度的鲁棒参数估计方法。作为示例，获得了基于Kullback Leibler散度的结果。仿真结果和两个数值例子说明了所提出方法的优点。

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