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A general robust t-process regression model
Computational Statistics & Data Analysis ( IF 1.8 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.csda.2020.107093
Zhanfeng Wang , Maengseok Noh , Youngjo Lee , Jian Qing Shi

Abstract The Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the current definitions of heavy-tailed processes, the unknown process regression function and the random errors are always defined jointly. This definition, mainly owing to mix-up of the regression function modeling and the distribution of the random errors, is not justified in many practical problems and thus limits the application of those robust approaches. It also results in a limitation of the statistical properties and robust analysis. A general robust process regression model is proposed by separating the nonparametric regression model from the distribution assumption of the random error. An efficient estimation procedure is developed. It shows that the estimated random-effects are useful in detecting outlying curves. Statistical properties, such as unbiasedness and information consistency, are provided. Numerical studies show that the proposed method is robust against outliers and outlying curves, and has a better performance in prediction compared with the existing models.

中文翻译:

一般稳健的 t 过程回归模型

摘要 众所周知,高斯过程回归 (GPR) 模型容易受到异常值的影响。已经开发了基于 t 过程或其他重尾过程的稳健过程回归模型来解决这个问题。然而,由于重尾过程的当前定义,未知过程回归函数和随机误差总是联合定义的。这个定义主要是由于回归函数建模和随机误差分布的混淆,在许多实际问题中是不合理的,因此限制了这些鲁棒方法的应用。它还导致统计特性和稳健分析的局限性。通过将非参数回归模型与随机误差的分布假设分离,提出了一种通用的鲁棒过程回归模型。开发了一种有效的估计程序。它表明估计的随机效应可用于检测异常曲线。提供了统计属性,例如无偏性和信息一致性。数值研究表明,所提出的方法对异常值和离群曲线具有鲁棒性,并且与现有模型相比具有更好的预测性能。
更新日期:2021-02-01
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