Abstract

Regression modelling where explanatory variables are measured with error is a common problem in applied sciences. However, if inappropriate analysis methods are applied, then unreliable conclusions can be made. This work deals with estimation and diagnostic analytics in regression modelling based on the Birnbaum–Saunders distribution using additive measurement errors. The maximum pseudo-likelihood and regression calibration methods are used for parameter estimation. We also carry out a residual analysis and apply global and local diagnostic techniques in order to detect anomalous and potentially influential observations. Simulations are conducted to validate the proposed approach and to evaluate performance. A real-world data set, related to earthquakes, is used to illustrate the new approach.

中文翻译：

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基于伯恩鲍姆-桑德斯分布的变量误差模型及其诊断方法在地震数据中的应用

摘要

在应用科学中，回归模型中的解释变量带有误差的测量是一个普遍的问题。但是，如果使用了不适当的分析方法，则可能得出不可靠的结论。这项工作基于Birnbaum–Saunders分布（使用加法测量误差）处理回归建模中的估计和诊断分析。最大伪似然法和回归校准方法用于参数估计。我们还进行残差分析并应用全局和局部诊断技术，以检测异常和可能有影响的观察结果。进行仿真以验证所提出的方法并评估性能。与地震有关的真实数据集用于说明新方法。